Sasakian 3-Metric as a $\ast$-Conformal Ricci Soliton Represents a Berger Sphere
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In this article, the notion of $\ast$-conformal Ricci soliton is defined as a self similar solution of the $\ast$-conformal Ricci flow. A Sasakian 3-metric satisfying the $\ast$-conformal Ricci soliton 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.
Abstract
In this article, the notion of $\ast$-conformal Ricci soliton is defined as a self similar solution of the $\ast$-conformal Ricci flow. A Sasakian 3-metric satisfying the $\ast$-conformal Ricci soliton 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.
참고문헌 (11)
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