Conditions of parallelism of *-Ricci tensor of three dimensional real hypersurfaces in non-flat complex space forms

TL;DR

This paper investigates the conditions under which the *-Ricci tensor of three-dimensional real hypersurfaces in non-flat complex space forms is parallel, extending previous results and introducing new findings on $\xi$-parallelism.

Contribution

It extends existing results on *-Ricci tensor conditions and introduces new results on $\xi$-parallelism for real hypersurfaces in non-flat complex space forms.

Findings

Extended results for vanishing, semi-parallel, and pseudo-parallel *-Ricci tensor cases.

New results on $\xi$-parallelism of *-Ricci tensor.

Characterized conditions for parallelism of *-Ricci tensor in the given setting.

Abstract

This paper focuses on the study of three dimensional real hypersurfaces in non-flat complex space forms whose $^{*}$-Ricci tensor satisfies conditions of parallelism. More precisely, extension of existing results concerning real hypersurfaces with vanishing, semi-parallel and pseudo-parallel $^{*}$-Ricci tensor in case of ambient space being the complex hyperbolic space are provided. Furthermore, new results concerning $\xi$-parallelism of $^{*}$-Ricci tensor of real hypersurfaces in non-flat complex space forms are presented.