Notes on Ricci solitons in $f$-cosymplectic manifolds

TL;DR

This paper investigates Ricci solitons on $f$-cosymplectic manifolds, focusing on contact and gradient types, providing classifications and properties of these geometric structures.

Contribution

It offers the first local classifications of $f$-cosymplectic manifolds admitting gradient Ricci solitons and explores properties related to contact Ricci solitons.

Findings

Classification of $f$-cosymplectic manifolds with gradient Ricci solitons

Properties of $f$-cosymplectic manifolds related to Ricci solitons

Analysis of contact Ricci solitons in $f$-cosymplectic manifolds

Abstract

The purpose of this article is to study an $f$-cosymplectic manifold $M$ admitting Ricci solitons. Here we consider mainly two classes of Ricci solitons on $f$-cosymplectic manifolds. One is the class of contact Ricci solitons. The other is the class of gradient Ricci solitons, for which we give the local classifications of $M$. Meanwhile, we also give some properties of $f$-cosymplectic manifolds.