Ricci solitons and concurrent vector fields

By Bang‐Yen Chen, Sharief Deshmukh. 2014

52 citations recorded by the source corpus.

A Ricci soliton $(M^n,g,v,\lambda)$ 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 $\lambda=1$ on Euclidean hypersurfaces. Several applications of our results are also presented.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2a2e243081fcd9e79ea9a754598e63cc567ec5db

How researchers see this paper

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In Applied Mathematics

1. Sharief Deshmukh
2. Bang‐Yen Chen
3. Ion Mihai
4. Bayram Sahin
5. I. Hasegawa
6. Siraj Uddin

In Astronomy and Astrophysics

1. Sharief Deshmukh
2. Bang‐Yen Chen
3. Bayram Sahin

In Geometry and Topology

1. Bang‐Yen Chen
2. Sharief Deshmukh
3. Ion Mihai
4. I. Hasegawa

Citations in the corpus

• Yamabe and Quasi-Yamabe Solitons on Euclidean Submanifolds (2017, background): “Ricci solitons on Euclidean submanifolds arisen from such a vector field have been studied recently by the authors in [8, 9].”