Some relationships between intrinsic and extrinsic invariants of submanifolds in generalized S-space-forms

TL;DR

This paper derives inequalities relating intrinsic and extrinsic invariants of submanifolds in generalized S-space-forms, with applications to slant submanifolds, enhancing understanding of their geometric properties.

Contribution

It establishes new inequalities of Chen's type connecting curvature invariants and mean curvature in generalized S-space-forms, including equality characterizations and applications to slant submanifolds.

Findings

Derived inequalities linking sectional, Ricci, scalar curvatures with mean curvature.

Characterized cases of equality in these inequalities.

Applied results specifically to slant submanifolds.

Abstract

We establish some inequalities of Chen's type between certain intrinsic invariants (involving sectional, Ricci and scalar curvatures) and the squared mean curvature of submanifolds tangent to the structure vector fields of a generalized S-space-form and we discuss the equality cases of them. We apply the obtained results to slant submanifolds.