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\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.

DOI Code: 10.1285/i15900932v42n1p95

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

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