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SOME RESULTS ON CONCIRCULAR VECTOR FIELDS AND THEIR APPLICATIONS TO RICCI SOLITONS
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 Title & Authors
SOME RESULTS ON CONCIRCULAR VECTOR FIELDS AND THEIR APPLICATIONS TO RICCI SOLITONS
CHEN, BANG-YEN;
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 Abstract
A vector field on a Riemannian manifold (M, g) is called concircular if it satisfies for any vector X tangent to M, where is the Levi-Civita connection and is a non-trivial function on M. A smooth vector field on a Riemannian manifold (M, g) is said to define a Ricci soliton if it satisfies the following Ricci soliton equation: , where is the Lie-derivative of the metric tensor g with respect to , Ric is the Ricci tensor of (M, g) and is a constant. A Ricci soliton (M, g, , ) on a Riemannian manifold (M, g) is said to have concircular potential field if its potential field is a concircular vector field. In the first part of this paper we determine Riemannian manifolds which admit a concircular vector field. In the second part we classify Ricci solitons with concircular potential field. In the last part we prove some important properties of Ricci solitons on submanifolds of a Riemannian manifold equipped with a concircular vector field.
 Keywords
concircular vector field;Ricci soliton;submanifolds;Einstein manifold;concircular potential field;concurrent vector field;concircular curvature tensor;
 Language
English
 Cited by
1.
Some Results About Concircular and Concurrent Vector Fields On Pseudo-Kaehler Manifolds, Journal of Physics: Conference Series, 2016, 766, 012034  crossref(new windwow)
2.
Pseudo-Z symmetric space-times with divergence-free Weyl tensor and pp-waves, International Journal of Geometric Methods in Modern Physics, 2016, 13, 02, 1650015  crossref(new windwow)
3.
Rigidity of (m,ρ)-quasi Einstein manifolds, Mathematische Nachrichten, 2017  crossref(new windwow)
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