-Ricci soliton on GSSF with Sasakian metric

doi:10.1285/i15900932v42n1p95

$\ast$ -Ricci soliton on GSSF with Sasakian metric

Ram Shankar Gupta, Savita Rani

Abstract

We study generalized Sasakian-space-forms (GSSF) $M^{2n+1} (k_1, k_2, k_3)$ with Sasa\-kian metric admitting $\ast$ -Ricci soliton. We obtain that either such GSSF has $k_1=\frac{2n+1}{2n+2}$ , $k_2= k_3=-\frac{1}{2n+2}$ and $\ast$ -soliton is steady or $k_1=0$ , $k_2=k_3=-1$ and $\ast$ -soliton is expanding. Also, we provide some examples in support of results. Further, we give an example that GSSF with Sasakian metric with $k_1 \neq 0$ and $k_1 \neq \frac{2n+1}{2n+2}$ do not admit the $\ast$ -Ricci soliton.

DOI Code: 10.1285/i15900932v42n1p95

Keywords: *-Ricci soliton; Generalized Sasakian-space-forms; Sasakian manifolds; Positive-Sasakian; Null-Sasakian

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This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.

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