Some Ricci solitons on Kenmotsu manifold

Shanmukha, B.; Venkatesha, V.

doi:10.1007/s41478-020-00243-z

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2020

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“…First, Ghosh considered an almost contact metric, in particular, a Kenmotsu metric, as a Ricci soliton and proved that a 3-dimensional Kenmotsu metric as a Ricci soliton is of constant negative curvature −1 in [17], and for higher dimension, a Kenmotsu metric as a Ricci soliton is Einstein if the metric is η-Einstein [15] or the potential vector field V is contact, see [18]. Shanmukha-Venkatesha [26] studied Ricci semi-symmetric Kenmotsu manifolds with η-Ricci solitons, and Sabina et. al.…”

Section: Introductionmentioning

confidence: 99%

Almost $η$-Ricci solitons on Kenmotsu manifolds

Patra¹,

Rovenski²

2020

Preprint

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In this paper we characterize the Einstein metrics in such broader classes of metrics as almost η-Ricci solitons and η-Ricci solitons on Kenmotsu manifolds, and generalize some results of other authors. First, we prove that a Kenmotsu metric as an η-Ricci soliton is Einstein metric if either it is η-Einstein or the potential vector field V is an infinitesimal contact transformation or V is collinear to the Reeb vector field. Further, we prove that if a Kenmotsu manifold admits a gradient almost η-Ricci soliton with a Reeb vector field leaving the scalar curvature invariant, then it is an Einstein manifold. Finally, we present new examples of η-Ricci solitons and gradient η-Ricci solitons, which illustrate our results.

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