Some inequalities on hemi-slant product submanifolds in a cosymplectic manifold

TL;DR

This paper derives new inequalities involving the second fundamental form for hemi-slant product submanifolds in cosymplectic manifolds, extending previous work on CR-warped products and analyzing equality cases.

Contribution

It introduces inequalities for hemi-slant product submanifolds in cosymplectic manifolds, expanding the understanding of their geometric properties and relations to sectional curvature.

Findings

Inequality for the squared norm of the second fundamental form in terms of φ-sectional curvature.

Inequality for hemi-slant warped products in cosymplectic manifolds.

Analysis of the conditions for equality cases.

Abstract

Recently, M. Atcken studied Contact CR-warped prod- uct submanifolds in cosymplectic space forms and established gen- eral sharp inequalities for CR-warped products in a cosymplectic manifold [1]. In the present paper, we obtain an inequality for the squared norm of the second fundamental form in terms of constant ?$\phi$-sectional curvature for hemi-slant products in cosymplectic mani- folds. An inequality for hemi-slant warped products in a cosymplectc manifold is also given. The equality case is considered.