Sasakian Manifold and *-Ricci Tensor

TL;DR

This paper investigates the properties of the *-Ricci tensor on Sasakian manifolds, exploring conformally flat conditions, *-Ricci symmetry, and *-Ricci solitons to deepen understanding of their geometric structures.

Contribution

It introduces new studies on *-Ricci tensor conditions, including conformally flat, *-Ricci symmetric, and *-Ricci soliton structures on Sasakian manifolds.

Findings

Characterization of *-Ricci conformally flat Sasakian manifolds

Conditions for *-Ricci symmetry on Sasakian manifolds

Existence and properties of *-Ricci solitons in this setting

Abstract

The purpose of this paper is to study *-Ricci tensor on Sasakian manifold. Here, \phi-confomally flat and confomally flat *-\eta-Einstein Sasakian manifold are studied. Next, we consider *-Ricci symmetric conditon on Sasakian manifold. Finally, we study a special type of metric called *-Ricci soliton on Sasakian manifold.