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Sasakian Metric As A Ricci Soliton And Related Results, Ramesh Sharma, Amalendu Ghosh

Mathematics Faculty Publications

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.