Para-Sasakian manifolds and *-Ricci solitons

TL;DR

This paper investigates *-Ricci solitons on para-Sasakian manifolds, establishing conditions under which such manifolds are either D-homothetic to Einstein manifolds or have vanishing Ricci tensor with respect to the canonical paracontact connection.

Contribution

It characterizes para-Sasakian manifolds admitting *-Ricci solitons, revealing their geometric structure and linking them to Einstein manifolds or Ricci-flat conditions.

Findings

Para-Sasakian *-Ricci solitons imply D-homothety to Einstein manifolds.

Alternatively, the Ricci tensor vanishes with respect to the canonical paracontact connection.

Provides conditions for the geometric classification of such manifolds.

Abstract

In this paper we study a special type of metric called *-Ricci soliton on para-Sasakian manifold. We prove that if the para-Sasakian metric is a *-Ricci soliton on a manifold M, then M is either D-homothetic to an Einstein manifold, or the Ricci tensor of M with respect to the canonical paracontact connection vanishes.