Sasakian metric as a Ricci soliton and related results

Abstract

We prove the following results: (i) A Sasakian metric as a non-trivial Ricci soliton is null $\eta$-Einstein, and expanding. Such a characterization permits to identify the Sasakian metric on the Heisenberg group ${\mathcal{H}}^{2n+1}$ as an explicit example of (non-trivial) Ricci soliton of such type. (ii) If an $\eta$-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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Cited by in corpus (2)

• Sasakian Manifold and *-Ricci Tensor
• Ricci solitons in almost $f$-cosymplectic manifolds