Geometry, Contact manifolds, Solitons
We prove the following results: (i) a Sasakian metric as a non-trivial Ricci soliton is null η-Einstein, and expanding. Such a characterization permits us to identify the Sasakian metric on the Heisenberg group H2n+1 as an explicit example of (non-trivial) Ricci soliton of such type. (ii) If an η-Einstein contact metric manifold M has a vector field V leaving the structure tensor and the scalar curvature invariant, then either V is an infinitesimal automorphism, or M is D-homothetically fixed K-contact.
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Sharma, Ramesh and Ghosh, Amalendu, "Sasakian Metric as a Ricci Soliton and Related Results" (2014). Mathematics Faculty Publications. 5.
Sharma, R., and Ghosh, A. (2014).Sasakian metric as a Ricci Soliton and related results. Journal of Geometry and Physics 75, 1-6.