On the Generalised Ricci Solitons and Sasakian Manifolds

TL;DR

This paper explores conditions under which odd-dimensional Riemannian manifolds can simultaneously support Sasakian structures and satisfy generalized Ricci soliton equations, providing theoretical insights and examples.

Contribution

It establishes a necessary condition linking Sasakian structures with generalized Ricci solitons on odd-dimensional manifolds, along with illustrative examples.

Findings

Identifies a necessary condition for Sasakian manifolds to satisfy generalized Ricci soliton equations.

Provides explicit examples of manifolds meeting these conditions.

Abstract

In this note, we find a necessary condition on odd-dimensional Riemannian manifolds under which both of Sasakian structure and the generalised Ricci soliton equation are satisfied, and we give some examples.