Chen and Casorati curvature inequalities for the submanifolds of Quaternionic Kaehler manifolds endowed with Ricci quarter-symmetric metric connection

TL;DR

This paper establishes Chen's inequalities and generalized Casorati curvature inequalities for submanifolds within quaternionic Kaehler manifolds equipped with Ricci quarter-symmetric metric connections, advancing geometric inequality theory.

Contribution

It introduces new curvature inequalities specifically for submanifolds in quaternionic Kaehler manifolds with Ricci quarter-symmetric metric connections, extending previous geometric results.

Findings

Derived Chen's inequalities for the submanifolds.

Established generalized normalized Casorati curvature inequalities.

Enhanced understanding of curvature relations in quaternionic Kaehler geometry.

Abstract

In this paper, authors have established Chen's inequalities for the submanifolds of quaternionic Kaehler manifolds characterized by Ricci quarter-symmetric metric connection. Other than these inequalities, we have also derived generalized normalized Casorati curvature inequalities for the same submanifolds.