Ricci $\rho$-solitons on 3-dimensional $\eta$-Einstein almost Kenmotsu mandifolds

Sh. Azami; Gh. Fasihi-Ramandi

Ricci $\rho$-solitons on 3-dimensional $\eta$-Einstein almost Kenmotsu mandifolds

Differential Geometry 2019-02-22 v1

Authors: Sh. Azami , Gh. Fasihi-Ramandi

Abstract

In this paper the notion of Ricci $\rho$ -soliton as a generalization of Ricci soliton is defined. We are motivated by the Ricci-Bourguignon flow to define this concept. We show that if a 3- dimensional almost Kenmotsu Einstein manifold $M$ be a $\rho$ -soliton, then $M$ is a Kenmotsu manifold of constant sectional curvature $-1$ and the $\rho$ -soliton is expanding, with $\lambda =2$ .

Keywords

ricci rho-soliton ricci soliton almost kenmotsu manifold eta-einstein manifold ricci-bourguignon flow constant sectional curvature

Cite

@article{arxiv.1902.08176,
  title  = {Ricci $\rho$-solitons on 3-dimensional $\eta$-Einstein almost Kenmotsu mandifolds},
  author = {Sh. Azami and Gh. Fasihi-Ramandi},
  journal= {arXiv preprint arXiv:1902.08176},
  year   = {2019}
}

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