Yamabe Solitons on (LCS)$_n$-manifolds

TL;DR

This paper investigates the properties of (LCS)$_n$-manifolds equipped with Yamabe solitons, providing characterizations, curvature conditions, and a concrete example of a 3-dimensional manifold.

Contribution

It offers new characterizations and curvature conditions for (LCS)$_n$-manifolds with Yamabe solitons, including a specific example.

Findings

Characterization of steady Yamabe solitons on (LCS)$_n$-manifolds

Curvature conditions for (LCS)$_n$-manifolds with Yamabe solitons

Explicit construction of a 3D (LCS)$_n$-manifold satisfying the conditions

Abstract

The object of the present paper is to study some properties of (LCS)$_n$-manifolds whose metric is Yamabe soliton. We establish some characterization of (LCS)$_n$-manifolds when the soliton becomes steady. Next we have studied some certain curvature conditions of (LCS)$_n$-manifolds admitting Yamabe solitons. Lastly we construct a 3-dimensional (LCS)$_n$-manifold satisfying the results.