Classification of Ricci solitons on Euclidean hypersurfaces

TL;DR

This paper classifies Ricci solitons on Euclidean hypersurfaces that originate from the position vector field, providing a complete understanding of their structure in this geometric setting.

Contribution

It offers a complete classification of Ricci solitons on Euclidean hypersurfaces arising specifically from the position vector field, expanding the understanding of Ricci solitons with concurrent potential fields.

Findings

Complete classification of Ricci solitons on Euclidean hypersurfaces

Identification of conditions under which these solitons arise from the position vector field

Extension of previous studies on concurrent vector fields in Riemannian geometry

Abstract

A Ricci soliton $(M,g,v,\lambda)$ on a Riemannian manifold $(M,g)$ is said to have concurrent potential field if its potential field $v$ is a concurrent vector field. Ricci solitons arisen from concurrent vector fields on Riemannian manifolds were studied recently in \cite{CD2}. The most important concurrent vector field is the position vector field on Euclidean submanifolds. In this paper we completely classify Ricci solitons on Euclidean hypersurfaces arisen from the position vector field of the hypersurfaces.