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Mohamed Tahar Kadaoui Abbassi - One of the best experts on this subject based on the ideXlab platform.
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On g-Natural Conformal Vector Fields on Unit Tangent Bundles
Czechoslovak Mathematical Journal, 2020Co-Authors: Mohamed Tahar Kadaoui Abbassi, Noura AmriAbstract:We study conformal and Killing vector fields on the Unit Tangent bundle, over a Riemannian manifold, equipped with an arbitrary pseudo-Riemannian g -natural metric. We characterize the conformal and Killing conditions for classical lifts of vector fields and we give a full classification of conformal fiber-preserving vector fields on the Unit Tangent bundle endowed with an arbitrary pseudo-Riemannian Kaluza-Klein type metric.
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Natural Paracontact Magnetic Trajectories on Unit Tangent Bundles
Axioms, 2020Co-Authors: Mohamed Tahar Kadaoui Abbassi, Noura AmriAbstract:In this paper, we study natural paracontact magnetic trajectories in the Unit Tangent bundle, i.e., those that are associated to g-natural paracontact metric structures. We characterize slant natural paracontact magnetic trajectories as those satisfying a certain conservation law. Restricting to two-dimensional base manifolds of constant Gaussian curvature and to Kaluza–Klein type metrics on their Unit Tangent bundles, we give a full classification of natural paracontact slant magnetic trajectories (and geodesics).
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Natural Ricci Solitons on Tangent and Unit Tangent bundles
arXiv: Differential Geometry, 2019Co-Authors: Mohamed Tahar Kadaoui Abbassi, Noura AmriAbstract:Considering pseudo-Riemannian $g$-natural metrics on Tangent bundles, we prove that the condition of being Ricci soliton is hereditary in the sense that a Ricci soliton structure on the Tangent bundle gives rise to a Ricci soliton structure on the base manifold. Restricting ourselves to some class of pseudo-Riemannian $g$-natural metrics, we show that the Tangent bundle is a Ricci soliton if and only if the base manifold is flat and the potential vector field is a complete lift of a conformal vector field. We give then a classification of conformal vector fields on a flat Riemannian manifold. When Unit Tangent bundles over a constant curvature Riemannian manifold are endowed with pseudo-Riemannian Kaluza-Klein type metric, we give a classification of Ricci soliton structures whose potential vector fields are fiber-preserving, inferring the existence of some of them which are non Einstein.
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kaluza klein type ricci solitons on Unit Tangent sphere bundles
Differential Geometry and Its Applications, 2018Co-Authors: Mohamed Tahar Kadaoui Abbassi, Noura Amri, Giovanni CalvarusoAbstract:Abstract We consider g-natural pseudo-Riemannian metrics of Kaluza–Klein type on the Unit Tangent sphere bundle of a Riemannian manifold of constant sectional curvature and give necessary and sufficient conditions for these metrics to give rise to a Ricci soliton. On the one hand, we obtain a rigidity result in dimension three, showing that there are no nontrivial Ricci solitons among g-natural metrics of Kaluza–Klein type on the Unit Tangent sphere bundle of any Riemannian surface. On the other hand, while Ricci solitons determined by Tangential lifts remain trivial in arbitrary dimension, horizontal lifts of vector fields related to the geometry of the base manifold (namely, homothetic vector fields) produce nontrivial Ricci solitons metrics of Kaluza–Klein type. Gradient Ricci solitons of Kaluza–Klein type are also completely characterized.
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Kaluza–Klein type Ricci solitons on Unit Tangent sphere bundles
Differential Geometry and its Applications, 2018Co-Authors: Mohamed Tahar Kadaoui Abbassi, Noura Amri, Giovanni CalvarusoAbstract:Abstract We consider g-natural pseudo-Riemannian metrics of Kaluza–Klein type on the Unit Tangent sphere bundle of a Riemannian manifold of constant sectional curvature and give necessary and sufficient conditions for these metrics to give rise to a Ricci soliton. On the one hand, we obtain a rigidity result in dimension three, showing that there are no nontrivial Ricci solitons among g-natural metrics of Kaluza–Klein type on the Unit Tangent sphere bundle of any Riemannian surface. On the other hand, while Ricci solitons determined by Tangential lifts remain trivial in arbitrary dimension, horizontal lifts of vector fields related to the geometry of the base manifold (namely, homothetic vector fields) produce nontrivial Ricci solitons metrics of Kaluza–Klein type. Gradient Ricci solitons of Kaluza–Klein type are also completely characterized.
Giovanni Calvaruso - One of the best experts on this subject based on the ideXlab platform.
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kaluza klein type ricci solitons on Unit Tangent sphere bundles
Differential Geometry and Its Applications, 2018Co-Authors: Mohamed Tahar Kadaoui Abbassi, Noura Amri, Giovanni CalvarusoAbstract:Abstract We consider g-natural pseudo-Riemannian metrics of Kaluza–Klein type on the Unit Tangent sphere bundle of a Riemannian manifold of constant sectional curvature and give necessary and sufficient conditions for these metrics to give rise to a Ricci soliton. On the one hand, we obtain a rigidity result in dimension three, showing that there are no nontrivial Ricci solitons among g-natural metrics of Kaluza–Klein type on the Unit Tangent sphere bundle of any Riemannian surface. On the other hand, while Ricci solitons determined by Tangential lifts remain trivial in arbitrary dimension, horizontal lifts of vector fields related to the geometry of the base manifold (namely, homothetic vector fields) produce nontrivial Ricci solitons metrics of Kaluza–Klein type. Gradient Ricci solitons of Kaluza–Klein type are also completely characterized.
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Kaluza–Klein type Ricci solitons on Unit Tangent sphere bundles
Differential Geometry and its Applications, 2018Co-Authors: Mohamed Tahar Kadaoui Abbassi, Noura Amri, Giovanni CalvarusoAbstract:Abstract We consider g-natural pseudo-Riemannian metrics of Kaluza–Klein type on the Unit Tangent sphere bundle of a Riemannian manifold of constant sectional curvature and give necessary and sufficient conditions for these metrics to give rise to a Ricci soliton. On the one hand, we obtain a rigidity result in dimension three, showing that there are no nontrivial Ricci solitons among g-natural metrics of Kaluza–Klein type on the Unit Tangent sphere bundle of any Riemannian surface. On the other hand, while Ricci solitons determined by Tangential lifts remain trivial in arbitrary dimension, horizontal lifts of vector fields related to the geometry of the base manifold (namely, homothetic vector fields) produce nontrivial Ricci solitons metrics of Kaluza–Klein type. Gradient Ricci solitons of Kaluza–Klein type are also completely characterized.
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Paracontact metric structures on the Unit Tangent sphere bundle
Annali di Matematica Pura ed Applicata (1923 -), 2014Co-Authors: Giovanni Calvaruso, Verónica Martín-molinaAbstract:Starting from $g$-natural pseudo-Riemannian metrics of suitable signature on the Unit Tangent sphere bundle $T_1 M$ of a Riemannian manifold $(M,\langle,\rangle)$, we construct a family of paracontact metric structures. We prove that this class of paracontact metric structures is invariant under $\mathcal D$-homothetic deformations, and classify paraSasakian and paracontact $(\kappa,\mu)$-spaces inside this class. We also present a way to build paracontact $(\kappa,\mu)$-spaces from corresponding contact metric structures on $T_1 M$.
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$g$-natural metrics of constant curvature on Unit Tangent sphere bundles
Archivum Mathematicum, 2012Co-Authors: Mohamed Tahar Kadaoui Abbassi, Giovanni CalvarusoAbstract:We completely classify Riemannian $g$-natural metrics of constant sectional curvature on the Unit Tangent sphere bundle $T_1 M$ of a Riemannian manifold $(M,g)$. Since the base manifold $M$ turns out to be necessarily two-dimensional, weaker curvature conditions are also investigated for a Riemannian $g$-natural metric on the Unit Tangent sphere bundle of a Riemannian surface.
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The Curvature Tensor of g-Natural Metrics on Unit Tangent Sphere Bundles
2008Co-Authors: Mohamed Tahar Kadaoui Abbassi, Giovanni CalvarusoAbstract:We calculate the curvature tensor of an arbitrary Riemannian gnatural metric on the Unit Tangent sphere bundle T1M of a Riemannian manifold M . This calculation is the fundamental tool to generalize classical theorems on the Unit Tangent sphere bundle, equipped with either the Sasaki metric or the standard contact metric structure. Mathematics Subject Classification: 53C15, 53C25, 53D10
Yusuf Yayli - One of the best experts on this subject based on the ideXlab platform.
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N-Legendre and N-slant curves in the Unit Tangent bundle of Minkowski surfaces
Asian-European Journal of Mathematics, 2017Co-Authors: Murat Bekar, Fouzi Hathout, Yusuf YayliAbstract:Let [Formula: see text] be a Unit Tangent bundle of Minkowski surface [Formula: see text] endowed with the pseudo-Riemannian induced Sasaki metric. In this present paper, we studied the N-Legendre and N-slant curves in which the inner product of its normal vector and Reeb vector is zero and nonzero constant, respectively, in [Formula: see text] and several important characterizations of these curves are given.
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N-Legendre and N-slant curves in the Unit Tangent bundle of Minkowski surfaces
Asian-european Journal of Mathematics, 2017Co-Authors: Murat Bekar, Fouzi Hathout, Yusuf YayliAbstract:Let (T1𝕄12,g 1) be a Unit Tangent bundle of Minkowski surface (𝕄12,g) endowed with the pseudo-Riemannian induced Sasaki metric. In this present paper, we studied the N-Legendre and N-slant curves in which the inner product of its normal vector and Reeb vector is zero and nonzero constant, respectively, in T1𝕄12,g 1 and several important characterizations of these curves are given.
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N-Legendre and N-slant curves in the Unit Tangent bundle of surfaces
kuwait journal of science, 2017Co-Authors: Fouzi Hathout, Murat Bekar, Yusuf YayliAbstract:Let (T1M; g1) be a Unit Tangent bundle of some surface (M; g) en-dowed with the induced Sasaki metric. In this present paper, we de- ne two kinds of curves called N-legendre and N-slant curves as curveshaving an inner product of normal vector and Reeb vector zero andnonzero constant respectively and several important characterizationsof these curves are obtained.
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legendre curves and singularities of a ruled surface according to rotation minimizing frame
arXiv: Differential Geometry, 2017Co-Authors: Murat Bekar, Fouzi Hathout, Yusuf YayliAbstract:In this paper, Legendre curves on Unit Tangent bundle are given using rotation minimizing (RM) vector fields. Ruled surfaces corresponding to these curves are represented. Singularities of these ruled surfaces are also analyzed and classifed.
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Lie Algebra of Unit Tangent Bundle
Advances in Applied Clifford Algebras, 2016Co-Authors: Murat Bekar, Yusuf YayliAbstract:In this paper, semi-quaternions are studied with their basic properties. Unit Tangent bundle of \({{\mathbb {R}}^2}\) is also obtained by using Unit semi-quaternions and it is shown that the set \({{T {\mathbb {R}}^2}}\) of all Unit semi-quaternions based on the group operation of semi-quaternion multiplication is a Lie group. Furthermore, the vector space matrix of angular velocity vectors forming the Lie algebra \({{T_{1} {\mathbb {R}}^2}}\) of the group \({{T {\mathbb {R}}^2}}\) is obtained. Finally, it is shown that the rigid body displacements obtained by using semi-quaternions correspond to planar displacements in \({{\mathbb {R}^3}}\).
Noura Amri - One of the best experts on this subject based on the ideXlab platform.
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On g-Natural Conformal Vector Fields on Unit Tangent Bundles
Czechoslovak Mathematical Journal, 2020Co-Authors: Mohamed Tahar Kadaoui Abbassi, Noura AmriAbstract:We study conformal and Killing vector fields on the Unit Tangent bundle, over a Riemannian manifold, equipped with an arbitrary pseudo-Riemannian g -natural metric. We characterize the conformal and Killing conditions for classical lifts of vector fields and we give a full classification of conformal fiber-preserving vector fields on the Unit Tangent bundle endowed with an arbitrary pseudo-Riemannian Kaluza-Klein type metric.
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Natural Paracontact Magnetic Trajectories on Unit Tangent Bundles
Axioms, 2020Co-Authors: Mohamed Tahar Kadaoui Abbassi, Noura AmriAbstract:In this paper, we study natural paracontact magnetic trajectories in the Unit Tangent bundle, i.e., those that are associated to g-natural paracontact metric structures. We characterize slant natural paracontact magnetic trajectories as those satisfying a certain conservation law. Restricting to two-dimensional base manifolds of constant Gaussian curvature and to Kaluza–Klein type metrics on their Unit Tangent bundles, we give a full classification of natural paracontact slant magnetic trajectories (and geodesics).
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Natural Ricci Solitons on Tangent and Unit Tangent bundles
arXiv: Differential Geometry, 2019Co-Authors: Mohamed Tahar Kadaoui Abbassi, Noura AmriAbstract:Considering pseudo-Riemannian $g$-natural metrics on Tangent bundles, we prove that the condition of being Ricci soliton is hereditary in the sense that a Ricci soliton structure on the Tangent bundle gives rise to a Ricci soliton structure on the base manifold. Restricting ourselves to some class of pseudo-Riemannian $g$-natural metrics, we show that the Tangent bundle is a Ricci soliton if and only if the base manifold is flat and the potential vector field is a complete lift of a conformal vector field. We give then a classification of conformal vector fields on a flat Riemannian manifold. When Unit Tangent bundles over a constant curvature Riemannian manifold are endowed with pseudo-Riemannian Kaluza-Klein type metric, we give a classification of Ricci soliton structures whose potential vector fields are fiber-preserving, inferring the existence of some of them which are non Einstein.
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kaluza klein type ricci solitons on Unit Tangent sphere bundles
Differential Geometry and Its Applications, 2018Co-Authors: Mohamed Tahar Kadaoui Abbassi, Noura Amri, Giovanni CalvarusoAbstract:Abstract We consider g-natural pseudo-Riemannian metrics of Kaluza–Klein type on the Unit Tangent sphere bundle of a Riemannian manifold of constant sectional curvature and give necessary and sufficient conditions for these metrics to give rise to a Ricci soliton. On the one hand, we obtain a rigidity result in dimension three, showing that there are no nontrivial Ricci solitons among g-natural metrics of Kaluza–Klein type on the Unit Tangent sphere bundle of any Riemannian surface. On the other hand, while Ricci solitons determined by Tangential lifts remain trivial in arbitrary dimension, horizontal lifts of vector fields related to the geometry of the base manifold (namely, homothetic vector fields) produce nontrivial Ricci solitons metrics of Kaluza–Klein type. Gradient Ricci solitons of Kaluza–Klein type are also completely characterized.
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Kaluza–Klein type Ricci solitons on Unit Tangent sphere bundles
Differential Geometry and its Applications, 2018Co-Authors: Mohamed Tahar Kadaoui Abbassi, Noura Amri, Giovanni CalvarusoAbstract:Abstract We consider g-natural pseudo-Riemannian metrics of Kaluza–Klein type on the Unit Tangent sphere bundle of a Riemannian manifold of constant sectional curvature and give necessary and sufficient conditions for these metrics to give rise to a Ricci soliton. On the one hand, we obtain a rigidity result in dimension three, showing that there are no nontrivial Ricci solitons among g-natural metrics of Kaluza–Klein type on the Unit Tangent sphere bundle of any Riemannian surface. On the other hand, while Ricci solitons determined by Tangential lifts remain trivial in arbitrary dimension, horizontal lifts of vector fields related to the geometry of the base manifold (namely, homothetic vector fields) produce nontrivial Ricci solitons metrics of Kaluza–Klein type. Gradient Ricci solitons of Kaluza–Klein type are also completely characterized.
Murat Bekar - One of the best experts on this subject based on the ideXlab platform.
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Lie Algebra of Unit Tangent Bundle in Minkowski 3-Space
International Electronic Journal of Geometry, 2019Co-Authors: Murat BekarAbstract:In this paper, a one-to-one correspondence between the set of Unit split semi-quaternions and Unit Tangent bundle of semi-Euclidean plane is given. It is shown that the set of Unit split semiquaternions based on the group operation of multiplication is a Lie group. The Lie algebra of this group, consisting of the vector space matrix of the angular velocity vectors, is also considered. Planar rotations in Euclidean plane are expressed using split semi-quaternions. Some examples are given to illustrate the findings.
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N-Legendre and N-slant curves in the Unit Tangent bundle of Minkowski surfaces
Asian-European Journal of Mathematics, 2017Co-Authors: Murat Bekar, Fouzi Hathout, Yusuf YayliAbstract:Let [Formula: see text] be a Unit Tangent bundle of Minkowski surface [Formula: see text] endowed with the pseudo-Riemannian induced Sasaki metric. In this present paper, we studied the N-Legendre and N-slant curves in which the inner product of its normal vector and Reeb vector is zero and nonzero constant, respectively, in [Formula: see text] and several important characterizations of these curves are given.
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N-Legendre and N-slant curves in the Unit Tangent bundle of Minkowski surfaces
Asian-european Journal of Mathematics, 2017Co-Authors: Murat Bekar, Fouzi Hathout, Yusuf YayliAbstract:Let (T1𝕄12,g 1) be a Unit Tangent bundle of Minkowski surface (𝕄12,g) endowed with the pseudo-Riemannian induced Sasaki metric. In this present paper, we studied the N-Legendre and N-slant curves in which the inner product of its normal vector and Reeb vector is zero and nonzero constant, respectively, in T1𝕄12,g 1 and several important characterizations of these curves are given.
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N-Legendre and N-slant curves in the Unit Tangent bundle of surfaces
kuwait journal of science, 2017Co-Authors: Fouzi Hathout, Murat Bekar, Yusuf YayliAbstract:Let (T1M; g1) be a Unit Tangent bundle of some surface (M; g) en-dowed with the induced Sasaki metric. In this present paper, we de- ne two kinds of curves called N-legendre and N-slant curves as curveshaving an inner product of normal vector and Reeb vector zero andnonzero constant respectively and several important characterizationsof these curves are obtained.
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legendre curves and singularities of a ruled surface according to rotation minimizing frame
arXiv: Differential Geometry, 2017Co-Authors: Murat Bekar, Fouzi Hathout, Yusuf YayliAbstract:In this paper, Legendre curves on Unit Tangent bundle are given using rotation minimizing (RM) vector fields. Ruled surfaces corresponding to these curves are represented. Singularities of these ruled surfaces are also analyzed and classifed.
