Real hypersurfaces with $^{*}$-Ricci solitons of non-flat complex space forms

TL;DR

This paper investigates real hypersurfaces in non-flat complex space forms that admit $^*$-Ricci solitons, focusing on cases where the potential vector field lies in specific geometric distributions, extending previous work on structure vector fields.

Contribution

It extends the study of $^*$-Ricci solitons by considering potential vector fields in principal curvature spaces and the holomorphic distribution, beyond the structure vector field.

Findings

Characterization of real hypersurfaces admitting $^*$-Ricci solitons with potential in principal curvature space.

Analysis of $^*$-Ricci solitons with potential in the holomorphic distribution.

Conditions under which such hypersurfaces exist and their geometric properties.

Abstract

Kaimakamis and Panagiotidou in \cite{KP} introduced the notion of $^*$-Ricci soliton and studied the real hypersurfaces of a non-flat complex space form admitting a $^*$-Ricci soliton whose potential vector field is the structure vector field. In this article, we consider that a real hypersurface of a non-flat complex space form admits a $^*$-Ricci soliton whose potential vector field belongs to the principal curvature space and the holomorphic distribution.