Parallel *-Ricci tensor of real hypersurfaces in CP^2 and CH^2

TL;DR

This paper proves the non-existence of three-dimensional real hypersurfaces with parallel *-Ricci tensor in non-flat complex space forms, and suggests directions for future research on *-Ricci tensors.

Contribution

It establishes a non-existence result for certain hypersurfaces with parallel *-Ricci tensor in complex space forms, advancing understanding in differential geometry.

Findings

No three-dimensional real hypersurfaces with parallel *-Ricci tensor exist in non-flat complex space forms.

Provides ideas for future research on *-Ricci tensor properties.

Contributes to the classification of hypersurfaces in complex geometry.

Abstract

The non-existence of three dimensional real hypersurfaces in non-flat complex space forms with parallel *-Ricci tensor is proved.At the end of the papaer ideas for further research on *-Ricci tensor are provided.