Riemannian Submersions Whose Total Manifolds Admitting a Ricci Soliton

TL;DR

This paper investigates Riemannian submersions with total manifolds that admit Ricci solitons, providing characterizations of fibers and conditions for the base manifold to also be a Ricci soliton, along with harmonicity criteria.

Contribution

It offers new characterizations of fibers and base manifolds in Riemannian submersions with Ricci soliton total spaces, including harmonicity conditions.

Findings

Fibers of such submersions are Ricci or almost Ricci solitons.

Necessary conditions for the base manifold to be a Ricci soliton are established.

Criteria for harmonicity of the submersion are provided.

Abstract

In this paper, we study Riemannian submersions whose total manifolds admitting a Ricci soliton. Here, we characterize any fiber of such a submersion is Ricci soliton or almost Ricci soliton. Indeed, we obtain necessary conditions for which the target manifold of Riemannian submersion is a Ricci soliton. Moreover, we study the harmonicity of Riemannian submersion from Ricci soliton and give a characterization for such a submersion to be harmonic.