On Submanifolds of Riemannian Manifolds Admitting a Ricci Soliton

Abstract

The aim of this paper is to study the conditions under which a submanifold of a Ricci soliton is also a Ricci soliton or an almost Ricci soliton. We give here a classification for Ricci solitons and their submanifolds according to their expanding, shrinking or steady cases.

Keywords

• ricci soliton
• riemannian submanifold
• curvature