Ricci solitons and concurrent vector fields
نویسندگان
چکیده
A Ricci soliton (M, g, v, λ) on a Riemannian manifold (M, 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 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 completely classify shrinking Ricci solitons with λ = 1 on Euclidean hypersurfaces. Several applications of our results are also presented. M.S.C. 2010: 53C25, 53C40.
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