On warped product semi-slant submanifolds of nearly Trans-Sasakian manifolds

Abstract

In this paper, we study warped product semi-slant submanifold of type M = N T × f N θ with slant fiber, isometrically immersed in a nearly Trans-Sasakian manifold by finding necessary and sufficient conditions in terms of Weingarten map. A characterization theorem is proved as main result.

On the Geometry of the Riemannian Curvature Tensor of Nearly Trans-Sasakian Manifolds

“…The next series of papers [18][19][20][21][22] is devoted to the study of a submanifold of a skew product of nearly trans-Sasakian manifolds. Conditions for the integrability of distributions on these submanifolds are obtained.…”

Geometry of Bi-Warped Product Submanifolds of Nearly Trans-Sasakian Manifolds

“…It has been noted that the class of bi-warped product submanifolds is a generalization of several classes, such as CR-warped products, warped product semi-slant submanifolds, and warped product pseudo-slant submanifolds. On the other hand, as a generalization of nearly cosymplectic, nearly Sasakian [13], nearly Kenmotsu [8,14], nearly α-Sasakian, and nearly β-Kenmotsu manifolds, nearly trans-Sasakian manifolds have been studied on a large scale; see [15][16][17][18][19]. Therefore, our objective was to remove the gap in the nearly trans-Sasakian manifold literature, as they are an interesting structure of the almost contact manifolds that have generalized many others structures.…”