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

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.