# Bulletin of theKorean Mathematical SocietyBKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

## Article

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Bull. Korean Math. Soc. 2022; 59(1): 101-110

Published online January 31, 2022 https://doi.org/10.4134/BKMS.b210125

## Sasakian 3-Metric as a $\ast$-Conformal Ricci Soliton Represents a Berger Sphere

Dibakar Dey

### 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.

Keywords: Sasakian 3-manifold, $\ast$-conformal Ricci soliton, infinitesimal contact transformation, infinitesimal automorphism, Berger sphere, Fano manifold

MSC numbers: Primary 53C25; Secondary 35Q51

Supported by: The author is thankful to the Council of Scienti c and Industrial Research, India (File No.
09/028(1010)/2017-EMR-1) for their assistance in the form of Senior Research
Fellowship.