Generalized Wintgen inequalities for submanifolds of conformally flat manifolds

TL;DR

This paper extends Wintgen inequalities to submanifolds within conformally flat manifolds, providing new theoretical bounds and exploring equality conditions with applications to manifolds of quasi-constant curvature.

Contribution

It introduces generalized Wintgen inequalities for submanifolds in conformally flat manifolds, expanding the theoretical framework and analyzing equality cases.

Findings

Derived generalized Wintgen inequalities for conformally flat manifolds

Provided applications to submanifolds in quasi-constant curvature spaces

Analyzed conditions for equality cases in the inequalities

Abstract

We obtain generalized Wintgen inequalities for submanifolds in conformally flat manifolds. We give some applications for submanifolds in a Riemannian manifold of quasi-constant curvature. Equality cases are also considered.