Some Inequalities Related to Ricci Curvatures for Lagrangian Submanifolds of Kahler QCH-manifolds

TL;DR

This paper derives new inequalities involving Ricci curvatures for Lagrangian submanifolds within Kähler QCH-manifolds, extending previous results from complex space forms.

Contribution

It establishes two general quadratic inequalities that lead to new Ricci curvature inequalities for Lagrangian submanifolds in Kähler QCH-manifolds, broadening existing geometric bounds.

Findings

Derived inequalities generalizing known results

Established quadratic inequalities for Ricci curvatures

Extended curvature bounds to broader manifold classes

Abstract

By establishing two general quadratic inequalities, we obtain some inequalities related to Ricci curvatures for Lagrangian submanifolds of K$\ddot{\mathrm{a}}$hler QCH-manifolds, which generalize some results for Lagrangian submanifolds of complex space forms.