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Öğe Chen-Ricci inequalities for submanifolds of Riemannian and Kaehlerian product manifolds(Polish Acad Sciences Inst Mathematics-Impan, 2016) Kilic, Erol; Tripathi, Mukut Mani; Guelbahar, 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 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 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.
