On Submanifolds in a Riemannian Manifold with a Semi-Symmetric Non-Metric Connection

Abstract

In this paper, we study submanifolds in a Riemannian manifold with a semi-symmetric non-metric connection. We prove that the induced connection on a submanifold is also semi-symmetric non-metric connection. We consider the total geodesicness and minimality of a submanifold with respect to the semi-symmetric non-metric connection. We obtain the Gauss, Cadazzi, and Ricci equations for submanifolds with respect to the semi-symmetric non-metric connection.

The First Eigenvalue Estimates of Warped Product Pseudo-Slant Submanifolds

“…which is (2). Because of the terms which were left in (18), M ⊥ is a totally geodesic submanifold in M.…”

“…For contradict that warped product pseudo-slant submanifolds always not generalize CR-warped product submanifold which was show in [13]. However, some interesting inequalities have been obtained by many geometers (see [4,10,12,[16][17][18][19][20]) for distinct warped product submanifolds in the different types of ambient manifolds. In [5], Al-Solamy derived the inequality for mixed, totally geodesic warped product pseudo-slant submanifolds of type M = M θ × f M ⊥ , in a nearly cosymplectic manifold.…”

Geometries of manifolds equipped with a Ricci (projection-Ricci) quarter-symmetric connection

“…On the other hand, the geometries of manifolds associated with some types of a quarter-symmetric non-metric connection ( [3,5,19]), or with Ricci tensor satisfying certain condition were studied recently. As we know, for instance, that Y. J.…”

Chen Inequalities for Warped Product Pointwise Bi-Slant Submanifolds of Complex Space Forms and Its Applications

“…In [2,5,[20][21][22][23][24][25][26][27][28][29][30][31], the authors discuss the study of Einstein, contact metrics, and warped product manifolds for the above-mentioned problems. Furthermore, in regard to the collections of such inequalities, we referred to [12] and references therein.…”