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- Title
Ricci solitons and concurrent vector fields.
- Authors
Bang-Yen Chen; Deshmukh, Sharief
- Abstract
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.
- Subjects
RIEMANNIAN manifolds; RICCI flow; SOLITONS; VECTOR fields; POTENTIAL theory (Mathematics); HYPERSURFACES
- Publication
Balkan Journal of Geometry & Its Applications, 2015, Vol 20, Issue 1, p14
- ISSN
1224-2780
- Publication type
Article