Ricci curvature of submanifolds in locally conformal almost cosymplectic manifolds

TL;DR

This paper establishes inequalities relating intrinsic and extrinsic curvature invariants of submanifolds within locally conformal almost cosymplectic manifolds, extending geometric understanding of these structures.

Contribution

It introduces new inequalities involving scalar, Ricci, and $k$-Ricci curvatures and squared mean curvature for various submanifold types in these manifolds.

Findings

Derived inequalities for submanifolds with pointwise constant $\

Discussed equality cases for these inequalities.

Extended results to slant, invariant, anti-invariant, and CR-submanifolds.

Abstract

We obtain certain inequalities involving several intrinsic invariants namely scalar curvature, Ricci curvature and $k$-Ricci curvature, and main extrinsic invariant namely squared mean curvature for submanifolds in a locally conformal almost cosymplectic manifold with pointwise constant $% \phi $-sectional curvature. Applying these inequalities we obtain several inequalities for slant, invariant, anti-invariant and {\em CR}-submanifolds. The equality cases are also discussed.