Classification of Ricci solitons on Euclidean hypersurfaces

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.

21 pages;Differential Geometry; To appear in International Journal of Mathematics

References in corpus (2)

• Ricci Flow and the Poincare Conjecture
• Ricci solitons and concurrent vector fields