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∗-Ricci Soliton within the frame-work of Sasakian and $(κ, μ)$ -contact manifold

Amalendu Ghosh

Department of Mathematics, Chandernagore College, Hooghly 712 136 (W.B.), India

E-mail Address: aghosh_70@yahoo.com

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and

Dhriti Sundar Patra

Department of Mathematics, Jadavpur University, Kolkata 700 032, India

E-mail Address: dhritimath@gmail.com

Corresponding author.

Present address: Department of Mathematics, Birla Institute of Technology Mesra, Ranchi 835215, India

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https://doi.org/10.1142/S0219887818501207Cited by:35 (Source: Crossref)

Abstract

We prove that if a Sasakian metric is a ∗-Ricci Soliton, then it is either positive Sasakian, or null-Sasakian. Next, we prove that if a complete Sasakian metric is an almost gradient ∗-Ricci Soliton, then it is positive-Sasakian and isometric to a unit sphere $S^{2 n + 1}$ . Finally, we classify nontrivial ∗-Ricci Solitons on non-Sasakian $(κ, μ)$ -contact manifolds.

Keywords:

AMSC: 53C15, 53C25, 53D10

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