Curvature inequalities for anti-invariant submersion from quaternionic space forms

TL;DR

This paper derives curvature inequalities related to Ricci and scalar curvatures in anti-invariant Riemannian submersions from quaternionic space forms, providing conditions for equality cases and advancing understanding of geometric structures.

Contribution

It introduces new curvature inequalities for anti-invariant submersions from quaternionic space forms and analyzes their equality cases, expanding geometric analysis in this area.

Findings

Derived Ricci and scalar curvature inequalities

Established equality conditions for the inequalities

Provided new insights into the geometry of quaternionic submersions

Abstract

This paper focuses on deriving several curvature inequalities involving the Ricci and scalar curvatures of the horizontal and vertical distributions in anti-invariant Riemannian submersions from quaternionic space forms onto Riemannian manifolds. In addition, a Ricci curvature inequality for anti-invariant Riemannian submersions is established. The equality cases for all derived inequalities are also examined.