Slant submanifolds of quaternionic space forms

TL;DR

This paper investigates inequalities related to the $k$-Ricci curvature of slant submanifolds within quaternionic space forms and explores conditions that prevent certain quaternionic slant immersions based on normal bundle properties.

Contribution

It establishes new inequalities for $k$-Ricci curvature and provides obstructions to quaternionic slant immersions with unfull first normal bundle.

Findings

Derived inequalities for $k$-Ricci curvature of slant submanifolds.

Identified obstructions to quaternionic slant immersions with unfull first normal bundle.

Enhanced understanding of geometric constraints in quaternionic space forms.

Abstract

In this paper we establish some inequalities concerning the $k$-Ricci curvature of a slant submanifold in a quaternionic space form. We also obtain obstructions to the existence of quaternionic slant immersions in quaternionic space forms with unfull first normal bundle.