[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c190089

RICCI 𝜌-SOLITONS ON 3-DIMENSIONAL 𝜂-EINSTEIN ALMOST KENMOTSU MANIFOLDS

Azami, Shahroud (Department of Pure Mathematics Faculty of Science Imam Khomeini International University)
Fasihi-Ramandi, Ghodratallah (Department of Pure Mathematics Imam Khomeini International University)

Publication Information

Communications of the Korean Mathematical Society / v.35, no.2, 2020 , pp. 613-623 More about this Journal

Abstract

The notion of quasi-Einstein metric in theoretical physics and in relation with string theory is equivalent to the notion of Ricci soliton in differential geometry. Quasi-Einstein metrics or Ricci solitons serve also as solution to Ricci flow equation, which is an evolution equation for Riemannian metrics on a Riemannian manifold. Quasi-Einstein metrics are subject of great interest in both mathematics and theoretical physics. In this paper the notion of Ricci 𝜌-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 is a 𝜌-soliton, then M is a Kenmotsu manifold of constant sectional curvature -1 and the 𝜌-soliton is expanding with λ = 2.

Keywords

Almost Kenmotsu manifold; ${\rho}$ -Ricci soliton; ${\eta}$ -Einstein; generalized k-nullity distribution;

Citations & Related Records

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