Pointwise slant and pointwise semi-slant submanifolds in almost contact metric manifolds

TL;DR

This paper introduces and studies pointwise slant and semi-slant submanifolds in almost contact metric manifolds, exploring their properties, examples, and inequalities related to their second fundamental form.

Contribution

It generalizes existing submanifold notions, provides characterizations, topological properties, and inequalities for warped product submanifolds in various almost contact metric manifolds.

Findings

Characterization of pointwise slant and semi-slant submanifolds

Topological properties and examples of these submanifolds

Inequalities for the second fundamental form in warped products

Abstract

As a generalization of slant submanifolds and semi-slant submanifolds, we introduce the notions of pointwise slant submanifolds and pointwise semi-slant sunmanifolds of an almost contact metric manifold. We obtain a characterization at each notion, investigate the topological properties of pointwise slant submanifolds, and give some examples of them. We also consider some distributions on cosymplectic, Sasakian, Kenmotsu manifolds and deal with some properties of warped product pointwise semi-slant submanifolds. Finally, we give some inequalities for the squared norm of the second fundamental form in terms of a warping function and a semi-slant function for warped product submanifolds of cosymplectic, Sasakian, Kenmotsu manifolds.