Chen–Ricci inequalities for submanifolds of Riemannian and Kaehlerian product manifolds

Erol Kılıç¹ ; Mukut Mani Tripathi² ; Mehmet Gülbahar³

¹ Department of Mathematics Faculty of Science and Art İnönü University Malatya, Turkey
² Department of Mathematics Institute of Science Banaras Hindu University Varanasi, India
³ Department of Mathematics Faculty of Science and Art Siirt University Siirt, Turkey

Annales Polonici Mathematici, Tome 116 (2016) no. 1, pp. 37-56.

Résumé

Some 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.

Détail

DOI : 10.4064/ap3666-12-2015

Keywords: examples slant submanifolds almost product riemannian manifolds presented existence useful orthonormal basis proper slant submanifolds riemannian product manifold proved sectional curvature ricci curvature scalar curvature submanifolds locally product manifolds almost constant curvature obtained chen ricci inequalities involving ricci tensor squared mean curvature submanifolds locally product manifolds almost constant curvature established chen ricci inequalities different kinds submanifolds kaehlerian product manifolds given