Classification of conformal solitons in pseudo-Euclidean spaces

TL;DR

This paper provides a complete classification of conformal solitons on pseudo-Riemannian hypersurfaces in pseudo-Euclidean spaces, including Yamabe solitons, based on the position vector field.

Contribution

It offers the first comprehensive classification of conformal solitons and Yamabe solitons on pseudo-Riemannian hypersurfaces in pseudo-Euclidean spaces.

Findings

Classification of conformal solitons derived from the position vector field

Complete characterization of Yamabe solitons in the same setting

New insights into the geometric structure of pseudo-Riemannian hypersurfaces

Abstract

In this paper, we completely classify conformal solitons on pseudo-Riemannian hypersurfaces in pseudo-Euclidean spaces arisen from the position vector field. In particular, the classification of Yamabe solitons on pseudo-Riemannian hypersurfaces in pseudo-Euclidean spaces arisen from the position vector field can be obtained.