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Öğe A useful orthonormal basis on bi-slant submanifolds of almost Hermitian manifolds(Tamkang University, 2016) Gülbahar, Mehmet; Kiliç, Erol; Keleş, SadikIn this paper, we study bi-slant submanifolds of an almost Hermitian manifold for different cases. We introduce a new orthonormal basis on bi-slant submanifold, semi-slant submanifold and hemi-slant submanifold of an almost Hermitian manifold to compute Chen's main inequalities. We investigate these inequalities for semi-slant submanifolds, hemi-slant submanifolds and slant submanifolds of a generalized complex space form. We obtain some characterizations on such submanifolds of a complex space form. © 2016, Tamkang University. All rights reserved.Öğe Chen–Ricci inequalities for submanifolds of Riemannian and Kaehlerian product manifolds(Annales Polonici Mathematici, 2016) Kılıç, Erol; Tripathi, Mukut Mani; Gülbahar, MehmetSome examples of slant submanifolds of almost product Riemannian manifolds are presented. The existence of a useful orthonormal basis in proper slant submanifolds of a Riemannian product manifold is proved. The sectional curvature, the Ricci curvature and the scalar curvature of submanifolds of locally product manifolds of almost constant curvature are obtained. Chen–Ricci inequalities involving the Ricci tensor and the squared mean curvature for submanifolds of locally product manifolds of almost constant curvature are established. Chen–Ricci inequalities for different kinds of submanifolds of Kaehlerian product manifolds are also given.Öğe Inequalities for scalar curvature of pseudo-Riemannian submanifolds(Journal of Geometry and Physics, 2017) Tripathi, Mukut Mani; Gülbahar, Mehmet; Kılıç, Erol; Keleş, SadıkSome basic inequalities, involving the scalar curvature and the mean curvature, for a pseudo-Riemannian submanifold of a pseudo-Riemannian manifold are obtained. We also find inequalities for spacelike submanifolds. Equality cases are also discussed.Öğe SCREEN ISOTROPIC LEAVES ON LIGHTLIKE HYPERSURFACES OF A LORENTZIAN MANIFOLD(Bullettin of the Korean Mathematical Society, 2017) Gülbahar, MehmetIn the present paper, screen isotropic leaves on lightlike hypersurfaces of a Lorentzian manifold are introduced and studied which are inspired by the definition of isotropic immersions in the Riemannian context. Some examples of such leaves are mentioned. Furthermore, some relations involving curvature invariants are obtained.Öğe Screen isotropic leaves on lightlike hypersurfaces of a lorentzian manifold(Korean Mathematical Society, 2017) Gülbahar, MehmetIn the present paper, screen isotropic leaves on lightlike hypersurfaces of a Lorentzian manifold are introduced and studied which are inspired by the definition of isotropic immersions in the Riemannian context. Some examples of such leaves are mentioned. Furthermore, some relations involving curvature invariants are obtained. © 2017 Korean Mathematical Society.Öğe SHARP INEQUALITIES INVOLVING THE RICCI CURVATURE FOR RIEMANNIAN SUBMERSIONS(2017) Gülbahar, Mehmet; Eken Meriç, Şemsi; Kılıç, ErolIn this paper, we obtain sharp inequalities on Riemannian manifolds admitting a Riemannian submersion and give some characterizations using these inequalities. We improve Chen-Ricci inequality for Riemannian submersion and present some examples which satisfy this inequality.Öğe Some basic inequalities for submanifolds of nearly quasi-constant curvature manifolds(Differential Geometry and Dinamical Systems, 2014) Gülbahar, Mehmet; Kılıç, Erol; Keleş, Sadık; Tripathi, Mukut ManiCertain basic inequalities involving the squared mean curvature and one of the Ricci curvature, the scalar curvature and the sectional curvature for a submanifold of quasi-constant curvature manifolds and nearly quasi-constant curvature manifolds are obtained. Equality cases are also discussed.Öğe Some inequalities for riemannian submersions(Sciendo, 2017) Meriç, Semsi Eken; Gülbahar, Mehmet; Kılıç, ErolIn this paper, we start by studying the scalar curvature of two Riemannian manifolds admitting a Riemannian submersion. We establish a series of inequalities for Riemannian submersions. By using these inequalities, we derive several characterizations for Riemannian submersions. We show that the necessary conditions for a Riemannian submersion to be harmonic is to either have totally geodesic fibres or integrable horizontal distribution. © 2018, Universitatii Al.I.Cuza din Iasi. All rights reserved.Öğe Special proper pointwise slant surfaces of a locally product Riemannian manifold(Turkish Journal of Mathematics, 2015) Gülbahar, Mehmet; Kılıç, Erol; Saraçoğlu Çelik, SemraThe structure of pointwise slant submanifolds in an almost product Riemannian manifold is investigated and the special proper pointwise slant surfaces of a locally product manifold are introduced. A relation involving the squared mean curvature and the Gauss curvature of pointwise slant surface of a locally product manifold is proved. Two examples of proper pointwise slant surfaces of a locally product manifold, one of which is special and the other one is not special, are given.Öğe A USEFUL ORTHONORMAL BASIS ON BI-SLANT SUBMANIFOLDS OF ALMOST HERMITIAN MANIFOLDS(Tamkang Journal of Mathematics, 2016) Gülbahar, Mehmet; Kılıç, Erol; Keleş, SadıkIn this paper, we study bi-slant submanifolds of an almost Hermitian manifold for different cases. We introduce a new orthonormal basis on bi-slant submanifold, semi-slant submanifold and hemi-slant submanifold of an almost Hermitian manifold to compute Chen’s main inequalities. We investigate these inequalities for semi-slant submanifolds, hemi-slant submanifolds and slant submanifolds of a generalized complex space form. We obtain some characterizations on such submanifolds of a complex space form.
