The Experts below are selected from a list of 22938 Experts worldwide ranked by ideXlab platform
Hakan Mete Tastan - One of the best experts on this subject based on the ideXlab platform.
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biwarped product Submanifolds of a kahler manifold
arXiv: Differential Geometry, 2016Co-Authors: Hakan Mete TastanAbstract:We study biwarped product Submanifolds which are special cases of multiply warped product Submanifolds in Kahler manifolds. We observe the non-existence of such Submanifolds under some circumstances. We show that there exists a non-trivial biwarped product Submanifold of a certain type by giving an illustrate example. We also give a necessary and sufficient condition for such Submanifolds to be locally trivial. Moreover, we establish an inequality for the squared norm of the second fundamental form in terms of the warping functions for such Submanifolds. The equality case is also discussed.
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warped product skew semi invariantSubmanifolds of order 1 of a locallyproduct riemannian manifold
Turkish Journal of Mathematics, 2015Co-Authors: Hakan Mete TastanAbstract:We introduce warped product skew semi-invariant Submanifolds of order $1$ of a locally product Riemannian manifold. We give a necessary and sufficient condition for a skew semi-invariant Submanifold of order 1 to be a locally warped product. We also establish an inequality between the warping function and the squared norm of the second fundamental form for such Submanifolds. The equality case is also discussed.
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the geometry of hemi slant Submanifolds of a locally product riemannian manifold
Turkish Journal of Mathematics, 2015Co-Authors: Hakan Mete Tastan, Fatma OzdemirAbstract:In the present paper, we study hemi-slant Submanifolds of a locally product Riemannian manifold. We prove that the anti-invariant distribution involved in the definition of hemi-slant Submanifold is integrable and give some applications of this result. We get a necessary and sufficient condition for a proper hemi-slant Submanifold to be a hemi-slant product. We also study these types of Submanifolds with parallel canonical structures. Moreover, we give two characterization theorems for the totally umbilical proper hemi-slant Submanifolds. Finally, we obtain a basic inequality involving Ricci curvature and the squared mean curvature of a hemi-slant Submanifold of a certain type of locally product Riemannian manifolds.
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warped product skew semi invariant Submanifolds of order 1 of a locally product riemannian manifold
arXiv: Differential Geometry, 2014Co-Authors: Hakan Mete TastanAbstract:We introduce warped product skew semi-invariant Submanifolds of order $1$ of a locally product Riemannian manifold. We give a necessary and sufficient condition for skew semi-invariant Submanifold of order 1 to be a locally warped product. We also prove that the invariant distribution which is involved in the definition of the Submanifold is integrable under some restrictions. Moreover, we find an inequality between the warping function and the squared norm of the second fundamental form for such Submanifolds. Equality case is also discussed.
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the geometry of hemi slant Submanifolds of a locally product riemannian manifold
arXiv: Differential Geometry, 2014Co-Authors: Hakan Mete Tastan, Fatma OzdemirAbstract:In the present paper, we study hemi-slant Submanifolds of a locally product Riemannian manifold. We prove that the anti-invariant distribution which is involved in the definition of hemi-slant Submanifold is integrable and give some applications of this result. We get a necessary and sufficient condition for a proper hemi-slant Submanifold to be a hemi-slant product. We also study this type Submanifolds with parallel canonical structures. Moreover, we give two characterization theorems for the totally umbilical proper hemi-slant Submanifolds. Finally, we obtain a basic inequality involving Ricci curvature and the squared mean curvature of a hemi-slant Submanifold of a certain type locally product Riemannian manifold.
Micah Warren - One of the best experts on this subject based on the ideXlab platform.
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on the regularity of hamiltonian stationary lagrangian Submanifolds
Advances in Mathematics, 2019Co-Authors: Jingyi Chen, Micah WarrenAbstract:Abstract We prove a Morrey-type theorem for Hamiltonian stationary Lagrangian Submanifolds of C n : If a C 1 Lagrangian Submanifold is a critical point of the volume functional under Hamiltonian variations, then it must be real analytic. Locally, a Hamiltonian stationary Lagrangian Submanifold is determined geometrically by harmonicity of its Lagrangian phase function, or variationally by a nonlinear fourth order elliptic equation of the potential function whose gradient graph defines the Hamiltonian stationary Lagrangian Submanifolds locally. Our result shows that Morrey's theorem for minimal Submanifolds admits a complete fourth order analogue. We establish full regularity and removability of singular sets of capacity zero for weak solutions to the fourth order equation with C 1 , 1 norm below a dimensional constant, and to C 1 , 1 potential functions, under certain convexity conditions, whose Lagrangian phase functions are weakly harmonic.
Mehmet Atçeken - One of the best experts on this subject based on the ideXlab platform.
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warped product semi invariant Submanifolds in almost paracontact riemannian manifolds
Mathematical Problems in Engineering, 2009Co-Authors: Mehmet AtçekenAbstract:We show that there exist no proper warped product semi-invariant Submanifolds in almost paracontact Riemannian manifolds such that totally geodesic Submanifold and totally umbilical Submanifold of the warped product are invariant and anti-invariant, respectively. Therefore, we consider warped product semi-invariant Submanifolds in the form =⟂× by reversing two factor manifolds and ⟂. We prove several fundamental properties of warped product semi-invariant Submanifolds in an almost paracontact Riemannian manifold and establish a general inequality for an arbitrary warped product semi-invariant Submanifold. After then, we investigate warped product semi-invariant Submanifolds in a general almost paracontact Riemannian manifold which satisfy the equality case of the inequality.
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F-Invariant Submanifolds of Kaehlerian Product Manifold
Turkish Journal of Mathematics, 2004Co-Authors: Mehmet AtçekenAbstract:In this paper, the geometry of F-invariant Submanifolds of a Kaehlerian product manifold is studied. The fundamental properties of these Submanifolds are investigated such as pseudo umbilical, curvature invariant, totally geodesic, mixed geodesic Submanifold and locally decomposable Riemannian product manifold.
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On Invariant Submanifolds of Riemannian Warped Product Manifold
Turkish Journal of Mathematics, 2003Co-Authors: Mehmet Atçeken, Bayram Şahin, Erol KiliçAbstract:In this paper, we generalize the geometry of the invariant Submanifolds of Riemannian product manifold to the geometry of the invariant Submanifolds of Riemannian warped product manifold. We investigate some properties of an invariant Submanifolds of a Riemannian warped product manifold. We show that every invariant Submanifold of the Riemannian warped product manifold is a Riemannian warped product manifold. Also, we give a theorem on the pseudo-umbilical invariant Submanifold. Further, we obtain that integral manifolds on an invariant Submanifold are curvature-invariant Submanifolds. Finally, we give a necessary condititon on a totally umbilical invariant Submanifold to be totally geodesic.
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Semi-invariant Submanifolds of Riemannian product manifold.
2003Co-Authors: Bayram Şahin, Mehmet AtçekenAbstract:In this paper, the geometry of Submanifolds of a Riemannian product manifold is studied. Fundamental properties of these Submanifolds are investigated such as integrability of distributions, totally umbilical semi-invariant Submanifold. Finally, necessary and sucient conditions are given on a semi-invariant Submanifold of a Riemannian product manifold to be a locally Riemannian manifold.
Bengu Bayram - One of the best experts on this subject based on the ideXlab platform.
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coordinate finite type rotational surfaces in euclidean spaces
Filomat, 2014Co-Authors: Bengu BayramAbstract:Abstract. Submanifolds of coordinate finite-type were introduced in [11]. A Submanifold of a Euclidean space is called a coordinate finite-type Submanifold if its coordinate functions are eigenfunctions of ∆. In the present study we consider coordinate finite-type surfaces in E4. We give necessary and sufficient conditions for generalized rotation surfaces in E4 to become coordinate finite-type. We also give some special examples.
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coordinate finite type rotational surfaces in euclidean spaces
arXiv: Differential Geometry, 2013Co-Authors: Bengu Bayram, Kadri Arslan, N Onen, Betul BulcaAbstract:Submanifolds of coordinate finite-type were introduced in HV1. A Submanifold of a Euclidean space is called a coordinate finite-type Submanifold if its coordinate functions are eigenfunctions of {\Delta}. In the present study we consider coordinate finite-type surfaces in E^4. We give necessary and sufficient conditions for generalized rotation surfaces in E^4 to become coordinate finite-type. We also give some special examples.
Erol Kiliç - One of the best experts on this subject based on the ideXlab platform.
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lightlike Submanifolds of a semi riemannian product manifold with quarter symmetric non metric connection
International Electronic Journal of Geometry, 2016Co-Authors: Oguzhan Bahadir, Erol KiliçAbstract:We study lightlike Submanifolds of a semi-Riemannian product manifold. We introduce a class of lightlike Submanifolds called screen semi-invariant lightlike Submanifold. We consider lightlike Submanifolds with respect to a quarter symmetric non-metric connection which is determined by the product structure. We give some equivalent conditions for integrability of distributions with respect to the Levi-Civita connection of semi-Riemannian manifolds and the quarter-symmetric nonmetric connection, and we obtain some results.
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Radical Anti-Invariant Lightlike Submanifolds of Semi-Riemannian Product Manifolds
Turkish Journal of Mathematics, 2008Co-Authors: Erol Kiliç, Bayram ŞahinAbstract:We introduce radical anti-invariant lightlike Submanifolds of a semi Riemannian product manifold and give examples. After we obtain the conditions of integrability of distributions which are involved in the definition of radical anti-invariant lightlike Submanifolds, we investigate the geometry of leaves of distributions. We also obtain the induced connection is a metric connection and a radical anti-invariant lightlike Submanifold is a product manifold under certain conditions. Finally, we study totally umbilical radical anti-invariant lightlike Submanifolds and observe that they are totally geodesic under a condition.
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On Invariant Submanifolds of Riemannian Warped Product Manifold
Turkish Journal of Mathematics, 2003Co-Authors: Mehmet Atçeken, Bayram Şahin, Erol KiliçAbstract:In this paper, we generalize the geometry of the invariant Submanifolds of Riemannian product manifold to the geometry of the invariant Submanifolds of Riemannian warped product manifold. We investigate some properties of an invariant Submanifolds of a Riemannian warped product manifold. We show that every invariant Submanifold of the Riemannian warped product manifold is a Riemannian warped product manifold. Also, we give a theorem on the pseudo-umbilical invariant Submanifold. Further, we obtain that integral manifolds on an invariant Submanifold are curvature-invariant Submanifolds. Finally, we give a necessary condititon on a totally umbilical invariant Submanifold to be totally geodesic.
