Classification of generalized Yamabe solitons in Euclidean spaces

TL;DR

This paper classifies generalized Yamabe solitons on hypersurfaces in Euclidean spaces, encompassing various types like Yamabe and conformal gradient solitons, based on the position vector field.

Contribution

It provides a complete classification of generalized Yamabe solitons in Euclidean spaces, unifying multiple notions under a single framework.

Findings

Complete classification of generalized Yamabe solitons in Euclidean spaces.

Unified treatment of various Yamabe-related solitons.

Insights into the geometric structure of hypersurfaces with these solitons.

Abstract

In this paper, we consider generalized Yamabe solitons which include many notions, such as Yamabe solitons, almost Yamabe solitons, h-almost Yamabe solitons, gradient k-Yamabe solitons and conformal gradient solitons. We completely classify the generalized Yamabe solitons on hypersurfaces in Euclidean spaces arisen from the position vector field.