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∗-Ricci solitons and gradient almost ∗-Ricci solitons on Kenmotsu manifolds

  • Venkatesha EMAIL logo , Devaraja Mallesha Naik and H. Aruna Kumara
From the journal Mathematica Slovaca

Abstract

In this paper, we consider *-Ricci soliton in the frame-work of Kenmotsu manifolds. First, we prove that if (M, g) is a Kenmotsu manifold and g is a *-Ricci soliton, then soliton constant λ is zero. For 3-dimensional case, if M admits a *-Ricci soliton, then we show that M is of constant sectional curvature –1. Next, we show that if M admits a *-Ricci soliton whose potential vector field is collinear with the characteristic vector field ξ, then M is Einstein and soliton vector field is equal to ξ. Finally, we prove that if g is a gradient almost *-Ricci soliton, then either M is Einstein or the potential vector field is collinear with the characteristic vector field on an open set of M. We verify our result by constructing examples for both *-Ricci soliton and gradient almost *-Ricci soliton.


The second author (D.M.N.) is grateful to University Grants Commission, New Delhi (Ref. No.:20/12/2015(ii)EU-V) for financial support in the form of Junior Research Fellowship.


  1. Communicated by Július Korbaš

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Received: 2019-01-16
Accepted: 2019-04-15
Published Online: 2019-12-22
Published in Print: 2019-12-18

© 2019 Mathematical Institute Slovak Academy of Sciences

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