$$*$$-Critical point equation on a class of almost Kenmotsu manifolds

Dey, Dibakar; Majhi, Pradip

doi:10.1007/s00022-020-0529-4

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2020

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Cited by 2 publications

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“…In 2014, the notion of * -Ricci soliton [12] was introduced and further widely studied by several authors. In 2019, the notion of * -critical point equation [8] was introduced and further studied by the authors in [9]. In this paper, we study the notion of * -conformal Ricci soliton defined as Definition 1.1.…”

Section: Introductionmentioning

confidence: 99%

$N(k)$-contact metric as $\ast$-conformal Ricci soliton

Dey¹,

Majhi²

2020

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The aim of this paper is characterize a class of contact metric manifolds admitting * -conformal Ricci soliton. It is shown that if a (2n + 1)-dimensional N (k)-contact metric manifold M admits * -conformal Ricci soliton or * -conformal gradient Ricci soliton, then the manifold M is * -Ricci flat and locally isometric to the Riemannian of a flat (n + 1)-dimensional manifold and an n-dimensional manifold of constant curvature 4 for n > 1 and flat for n = 1. Further, for the first case, the soliton vector field is conformal and for the * -gradient case, the potential function f is either harmonic or satisfy a Poisson equation. Finally, an example is presented to support the results.

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Section: Introductionmentioning

confidence: 99%