Sasakian 3-Metric as a $\ast$-Conformal Ricci Soliton Represents a Berger Sphere
Bull. Korean Math. Soc.
Published online August 24, 2021
Dibakar Dey
University of Calcutta
Abstract : A $\ast$-conformal Ricci soliton is a self similar solution of the $\ast$-conformal Ricci flow. In this paper, a Sasakian 3-metric satisfying the $\ast$-conformal Ricci soltion is completely classified under certain conditions on the soliton vector field. We establish a relation with Fano manifolds and proves a homothety between the Sasakian 3-metric and the Berger Sphere. Also, the potential vector field $V$ is a harmonic infinitesimal automorphism of the contact metric structure.
Keywords : Sasakian 3-manifold, $\ast$-Conformal Ricci soliton, Infinitesimal contact transformation, Infinitesimal automorphism, Berger sphere, Fano manifold.
MSC numbers : 53C25, 35Q51
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