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arXiv · 1407.2790

Ricci solitons and concurrent vector fields

Bang-Yen Chen·Sharief Deshmukh
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Abstract

A Ricci soliton $(M^n,g,v,λ)$ on a Riemannian manifold $(M^n,g)$ 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.

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Bang-Yen Chen, Sharief Deshmukh. 2014-07-10. Ricci solitons and concurrent vector fields. https://arxiv.org/abs/1407.2790

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