The Experts below are selected from a list of 15033 Experts worldwide ranked by ideXlab platform
Mehmet Akif Akyol - One of the best experts on this subject based on the ideXlab platform.
-
New curvature tensors along Riemannian Submersions
arXiv: General Mathematics, 2020Co-Authors: Mehmet Akif Akyol, Gülhan AyarAbstract:In 1966, B. O'Neill [The fundamental equations of a Submersion, Michigan Math. J., Volume 13, Issue 4 (1966), 459-469.] obtained some fundamental equations and curvature relations between the total space, the base space and the fibres of a Submersion. In the present paper, we define new curvature tensors along Riemannian Submersions such as Weyl projective curvature tensor, concircular curvature tensor, conharmonic curvature tensor, conformal curvature tensor and $M-$projective curvature tensor, respectively. Finally, we obtain some results in case of the total space of Riemannian Submersions has umbilical fibres for any curvature tensors mentioned by the above.
-
On bi-slant Submersions in complex geometry
International Journal of Geometric Methods in Modern Physics, 2020Co-Authors: Cem Sayar, Mehmet Akif Akyol, Rajendra PrasadAbstract:In the present paper, we introduce bi-slant Submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalization of invariant, anti-invariant, semi-invariant, slant, semi-slant and hemi-slant Riemannian Submersions. We mainly focus on bi-slant Submersions from Kaehler manifolds. We provide a proper example of bi-slant Submersion, investigate the geometry of foliations determined by vertical and horizontal distributions, and obtain the geometry of leaves of these distributions. Moreover, we obtain curvature relations between the base space, the total space and the fibres, and find geometric implications of these relations.
-
Conformal slant Submersions from cosymplectic manifolds
TURKISH JOURNAL OF MATHEMATICS, 2018Co-Authors: Yılmaz Gündüzalp, Mehmet Akif AkyolAbstract:Akyol [Conformal anti-invariant Submersions from cosymplectic manifolds, Hacettepe Journal of Mathematics and Statistics 2017; 462: 177-192] defined and studied conformal antiinvariant Submersions from cosymplectic manifolds. The aim of the present paper is to define and study the notion of conformal slant Submersions (it means the Reeb vector field $\xi$ is a vertical vector field) from cosymplectic manifolds onto Riemannian manifolds as a generalization of Riemannian Submersions, horizontally conformal Submersions, slant Submersions, and conformal antiinvariant Submersions. More precisely, we mention many examples and obtain the geometries of the leaves of vertical distribution and horizontal distribution, including the integrability of the distributions, the geometry of foliations, some conditions related to total geodesicness, and harmonicity of the Submersions. Finally, we consider a decomposition theorem on the total space of the new Submersion.
-
Biharmonic Riemannian Submersions
Annali di Matematica Pura ed Applicata (1923 -), 2018Co-Authors: Mehmet Akif AkyolAbstract:In this paper, we study biharmonic Riemannian Submersions. We first derive bitension field of a general Riemannian Submersion, and we then use it to obtain biharmonic equations for Riemannian Submersions with one-dimensional fibers and Riemannian Submersions with basic mean curvature vector fields of fibers. These are used to construct examples of proper biharmonic Riemannian Submersions with one-dimensional fibers and to characterize warped products whose projections onto the first factor are biharmonic Riemannian Submersions.
-
Biharmonic Riemannian Submersions
arXiv: Differential Geometry, 2018Co-Authors: Mehmet Akif AkyolAbstract:In this paper, we study biharmonic Riemannian Submersions. We first derive bitension field of a general Riemannian Submersion, we then use it to obtain biharmonic equations for Riemannian Submersions with $1$-dimensional fibers and Riemannian Submersions with basic mean curvature vector fields of fibers. These are used to construct examples of proper biharmonic Riemannian Submersions with $1$-dimensional fibers and to characterize warped products whose projections onto the first factor are biharmonic Riemannian Submersions.
Yılmaz Gündüzalp - One of the best experts on this subject based on the ideXlab platform.
-
Conformal slant Submersions from cosymplectic manifolds
TURKISH JOURNAL OF MATHEMATICS, 2018Co-Authors: Yılmaz Gündüzalp, Mehmet Akif AkyolAbstract:Akyol [Conformal anti-invariant Submersions from cosymplectic manifolds, Hacettepe Journal of Mathematics and Statistics 2017; 462: 177-192] defined and studied conformal antiinvariant Submersions from cosymplectic manifolds. The aim of the present paper is to define and study the notion of conformal slant Submersions (it means the Reeb vector field $\xi$ is a vertical vector field) from cosymplectic manifolds onto Riemannian manifolds as a generalization of Riemannian Submersions, horizontally conformal Submersions, slant Submersions, and conformal antiinvariant Submersions. More precisely, we mention many examples and obtain the geometries of the leaves of vertical distribution and horizontal distribution, including the integrability of the distributions, the geometry of foliations, some conditions related to total geodesicness, and harmonicity of the Submersions. Finally, we consider a decomposition theorem on the total space of the new Submersion.
-
On the Geometry of Conformal Anti-invariant $\xi^\perp-$ Submersions
2018Co-Authors: Mehmet Akif Akyol, Yılmaz GündüzalpAbstract:Lee [Anti-invariant $\xi^{\perp}-$ Riemannian Submersions from almost contact manifolds, Hacettepe Journal of Mathematics and Statistic, 42(3), (2013), 231-241.] defined and studied anti-invariant $\xi^\perp-$ Riemannian Submersions from almost contact manifolds.The main goal of this paper is to consider conformal anti-invariant $\xi^\perp-$ Submersions (it means the Reeb vector field $\xi$ is a horizontal vector field) from almost contact metric manifolds onto Riemannian manifolds as a generalization of anti-invariant $\xi^\perp-$ Riemannian Submersions. More precisely, we obtain the geometries of the leaves of $\ker\pi_{*}$ and $(\ker\pi_{*})^\perp,$ including the integrability of the distributions, the geometry of foliations, some conditions related to totally geodesicness and harmonicty of the Submersions. Finally, we show that there are certain product structures on the total space of a conformal anti-invariant $\xi^\perp-$ Submersion.
-
SEMI-INVARIANT SEMI-RIEMANNIAN SubmersionS
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2018Co-Authors: Mehmet Akif Akyol, Yılmaz GündüzalpAbstract:In this paper, we introduce semi-invariant semi-Riemannian Submersions from para-Kahler manifolds onto semi-Riemannian manifolds. Wegive some examples, investigate the geometry of foliations that arise fromthe de…nition of a semi-Riemannian Submersion and check the harmonicity ofsuch Submersions. We also find necessary and su¢ cient conditions for a semiinvariant semi-Riemannian Submersion to be totally geodesic. Moreover, weobtain curvature relations between the base manifold and the total manifold
-
Conformal anti-invariant $\xi^\perp-$Submersions
arXiv: Differential Geometry, 2017Co-Authors: Mehmet Akif Akyol, Yılmaz GündüzalpAbstract:As a generalization of anti-invariant $\xi^\perp-$Riemannian Submersions, we introduce conformal anti-invariant $\xi^\perp-$Submersions from almost contact metric manifolds onto Riemannian manifolds. We investigate the geometry of foliations which are arisen from the definition of a conformal Submersion and find necessary and sufficient conditions for a conformal anti-invariant $\xi^\perp-$Submersion to be totally geodesic and harmonic, respectively. Moreover, we show that there are certain product structures on the total space of a conformal anti-invariant $\xi^\perp-$Submersion.
-
Almost para-Hermitian Submersions
Matematički Vesnik, 2016Co-Authors: Yılmaz GündüzalpAbstract:In this paper, we introduce the concept of almost para-Hermitian Submersions between almost para-Hermitian manifolds. We investigate the influence of a given structure defined on the total manifold on the determination of the corresponding structure on the base manifold. Moreover, we provide an example, investigate various properties of the O'Neill's tensors for such Submersions, find the integrability of the horizontal distribution and obtain necessary and sufficient conditions for the fibres of an almost para-Hermitian Submersion to be totally geodesic. We also obtain curvature relations between the base manifold and the total manifold.
Bayram Sahin - One of the best experts on this subject based on the ideXlab platform.
-
Conformal slant Submersions
Hacettepe Journal of Mathematics and Statistics, 2017Co-Authors: Mehmet Akif Akyol, Bayram SahinAbstract:As a generalization of conformal holomorphic Submersions and conformal anti-invariant Submersions, we introduce a new conformal Submersion from almost Hermitian manifolds onto Riemannian manifolds, namely conformal slant Submersions. We give examples and find necessary and sufficient conditions for such maps to be harmonic morphism. We also investigate the geometry of foliations which are arisen from the definition of a conformal Submersion and obtain a decomposition theorem on the total space of a conformal slant Submersion. Moreover, we find necessary and sufficient conditions of a conformal slant Submersion to be totally geodesic.
-
Conformal semi-invariant Submersions
Communications in Contemporary Mathematics, 2017Co-Authors: Mehmet Akif Akyol, Bayram SahinAbstract:As a generalization of semi-invariant Submersions, we introduce conformal semi-invariant Submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations which arise from the definition of a conformal Submersion and show that there are certain product structures on the total space of a conformal semi-invariant Submersion. Moreover, we also check the harmonicity of such Submersions and find necessary and sufficient conditions of a conformal semi-invariant Submersion to be totally geodesic.
-
Riemannian Maps From Almost Hermitian Manifolds
Riemannian Submersions Riemannian Maps in Hermitian Geometry and their Applications, 2017Co-Authors: Bayram SahinAbstract:In this chapter, we study Riemannian maps from almost Hermitian manifolds to Riemannian manifolds. In section 1, we study holomorphic Riemannian maps as a generalization of holomorphic Submersions and obtain a characterization of such maps. In section 2, we investigate anti-invariant Riemannian maps as a generalization of anti-invariant Submersion, investigate the geometry of leaves of distributions defined by such maps, and give necessary and sufficient conditions for anti-invariant Riemannian maps to be totally geodesic. We also find necessary and sufficient conditions for the total manifold of anti-invariant Riemannian maps to be an Einstein manifold. In section 3, as a generalization of the semi-invariant Submersion, we introduce semi-invariant Riemannian maps, give examples, and obtain the main properties of such maps. In section 4, we introduce generic Riemannian maps from almost Hermitian manifolds to Riemannian manifolds as a generalization of generic Submersions and we give examples. We also find new conditions for Riemannian maps to be totally geodesic and harmonic. In section 5, we study slant Riemannian maps as a generalization of slant Submersion, give examples, and obtain the harmonicity of such maps. We also find new necessary and sufficient conditions for such maps to be totally geodesic. Moreover, we obtain a decomposition theorem by slant Riemannian maps. In section 6, we define semi-slant Riemannian maps and give examples. In section 7, we introduce hemi-slant Riemannian maps as a generalization of hemi-slant Submersions and slant Riemannian maps, give examples, obtain integrability conditions for distribution, and investigate the geometry of these distributions. We also obtain conditions for such maps to be harmonic and totally geodesic, respectively.
-
EINSTEIN CONDITIONS FOR THE BASE SPACE OF ANTI-INVARIANT RIEMANNIAN SubmersionS AND CLAIRAUT SubmersionS
Taiwanese Journal of Mathematics, 2015Co-Authors: Jungchan Lee, Bayram Sahin, Jeonghyeong Park, Dae-yup SongAbstract:In this paper, we study the geometry of anti-invariant RiemannianSubmersions from a Kahler manifold onto a Riemannian manifold. Wefirst determine the base space when the total space of ananti-invariant Riemannian Submersion is Einstein and then weinvestigate new conditions for anti-invariant Riemannian Submersionsto be Clairaut Submersions. We also focus on the geometry ofClairaut anti-invariant Submersions.
-
Hemi-Slant Submersions
Mediterranean Journal of Mathematics, 2015Co-Authors: Hakan Mete Taştan, Bayram Sahin, Şener YananAbstract:As a generalization of anti-invariant Submersions, semi-invariant Submersions and slant Submersions, we introduce the notion of hemi-slant Submersion and study such Submersions from Kahlerian manifolds onto Riemannian manifolds. After we study the geometry of leaves of distributions which are involved in the definition of the Submersion, we obtain new conditions for such Submersions to be harmonic and totally geodesic. Moreover, we give a characterization theorem for the proper hemi-slant Submersions with totally umbilical fibers.
Ramazan Sari - One of the best experts on this subject based on the ideXlab platform.
-
on semi slant varvec xi perp riemannian Submersions
Mediterranean Journal of Mathematics, 2017Co-Authors: Mehmet Akif Akyol, Ramazan SariAbstract:The aim of the present paper is to define and study semi-slant \(\xi ^\perp \)-Riemannian Submersions from Sasakian manifolds onto Riemannian manifolds as a generalization of anti-invariant \(\xi ^\perp \)-Riemannian Submersions, semi-invariant \(\xi ^\perp \)-Riemannian Submersions and slant Riemannian Submersions. We obtain characterizations, investigate the geometry of foliations which arise from the definition of this new Submersion. After we investigate the geometry of foliations, we obtain necessary and sufficient condition for base manifold to be a locally product manifold and proving new conditions to be totally umbilical and totally geodesicness, respectively. Moreover, some examples of such Submersions are mentioned.
-
On Semi-Slant $${\varvec{\xi ^\perp }}$$-Riemannian Submersions
Mediterranean Journal of Mathematics, 2017Co-Authors: Mehmet Akif Akyol, Ramazan SariAbstract:The aim of the present paper is to define and study semi-slant \(\xi ^\perp \)-Riemannian Submersions from Sasakian manifolds onto Riemannian manifolds as a generalization of anti-invariant \(\xi ^\perp \)-Riemannian Submersions, semi-invariant \(\xi ^\perp \)-Riemannian Submersions and slant Riemannian Submersions. We obtain characterizations, investigate the geometry of foliations which arise from the definition of this new Submersion. After we investigate the geometry of foliations, we obtain necessary and sufficient condition for base manifold to be a locally product manifold and proving new conditions to be totally umbilical and totally geodesicness, respectively. Moreover, some examples of such Submersions are mentioned.
-
On semi-slant $\xi^\perp-$Riemannian Submersions
arXiv: Differential Geometry, 2017Co-Authors: Mehmet Akif Akyol, Ramazan SariAbstract:The aim of the present paper to define and study semi-slant $\xi^\perp-$Riemannian Submersions from Sasakian manifolds onto Riemannian manifolds as a generalization of anti-invariant $\xi^\perp-$Riemannian Submersions, semi-invariant $\xi^\perp-$Riemannian Submersions and slant Riemannian Submersions. We obtain characterizations, investigate the geometry of foliations which arise from the definition of this new Submersion. After we investigate the geometry of foliations, we obtain necessary and sufficient condition for base manifold to be a locally product manifold and proving new conditions to be totally umbilical and totally geodesicness, respectively. Moreover, some examples of such Submersions are mentioned.
Cengizhan Murathan - One of the best experts on this subject based on the ideXlab platform.
-
Riemannian Warped Product Submersions
Results in Mathematics, 2020Co-Authors: İrem Küpeli erken, Cengizhan MurathanAbstract:In this paper, we introduce Riemannian warped product Submersions and construct examples and give fundamental geometric properties of such Submersions. On the other hand, a necessary and sufficient condition for a Riemannian warped product Submersion to be totally geodesic, totally umbilic and minimal is given.
-
Slant Riemannian Submersions from Sasakian manifolds
Arab Journal of Mathematical Sciences, 2016Co-Authors: I. Küpeli Erken, Cengizhan MurathanAbstract:Abstract We introduce and characterize slant Riemannian Submersions from Sasakian manifolds onto Riemannian manifolds. We survey main results of slant Riemannian Submersions defined on Sasakian manifolds. We give a sufficient condition for a slant Riemannian Submersion from Sasakian manifolds onto Riemannian manifolds to be harmonic. We also give an example of such slant Submersions. Moreover, we find a sharp inequality between the scalar curvature and norm squared mean curvature of fibres.
-
Anti-Invariant Riemannian Submersions from Cosymplectic Manifolds
arXiv: Differential Geometry, 2013Co-Authors: Cengizhan Murathan, I. Küpeli ErkenAbstract:We introduce anti-invariant Riemannian Submersions from cosymplectic manifolds onto Riemannian manifolds. We survey main results of anti-invariant Riemannian Submersions defined on cosymplectic manifolds. We investigate necessary and sufficient condition for an anti-invariant Riemannian Submersion to be totally geodesic and harmonic. We give examples of anti-invariant Submersions such that characteristic vector field {\xi} is vertical or horizontal. Moreover we give decomposition theorems by using the existence of anti-invariant Riemannian Submersions.
-
Anti-Invariant Riemannian Submersions from Sasakian Manifolds
arXiv: Differential Geometry, 2013Co-Authors: I. Küpeli Erken, Cengizhan MurathanAbstract:We introduce anti-invariant Riemannian Submersions from Sasakian manifolds onto Riemannian manifolds. We survey main results of anti-invariant Riemannian Submersions defined on Sasakian manifolds. We investigate necessary and sufficient condition for an anti-invariant Riemannian Submersion to be totally geodesic and harmonic. We give examples of anti-invariant Submersions such that characteristic vector field {\xi} is vertical or horizontal.
