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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap3666-12-2015,
author = {Erol K\i l\i \c c and Mukut Mani Tripathi and Mehmet G\"ulbahar},
title = {Chen-Ricci inequalities for submanifolds of Riemannian and Kaehlerian product manifolds},
journal = {Annales Polonici Mathematici},
volume = {116},
year = {2016},
pages = {37-56},
zbl = {1337.53069},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3666-12-2015}
}
Erol Kılıç; Mukut Mani Tripathi; Mehmet Gülbahar. Chen-Ricci inequalities for submanifolds of Riemannian and Kaehlerian product manifolds. Annales Polonici Mathematici, Tome 116 (2016) pp. 37-56. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3666-12-2015/