Ricci solitons and concurrent vector fields

A Ricci soliton (Mⁿ, g, v, λ) on a Riemannian manifold (Mⁿ, g) is said to have concurrent potential field if its potential field v is a concurrent vector field. In the first part of this paper we completely classify Ricci solitons with concurrent potential fields. In the second part we derive a necessary and sufficient condition for a submanifold to be a Ricci soliton in a Riemannian manifold equipped with a concurrent vector field. In the last part, we classify shrinking Ricci solitons with λ=1 on Euclidean hypersurfaces. Several applications of our results are also presented.