Open AccessRicci soliton and Ricci almost soliton within the framework of Kenmotsu manifold
Author(s) -
Amalendu Ghosh
Publication year - 2019
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.11.1.59-69
Subject(s) - einstein manifold , mathematics , scalar curvature , ricci curvature , einstein , manifold (fluid mechanics) , vector field , soliton , mathematical physics , pure mathematics , invariant (physics) , invariant manifold , curvature , mathematical analysis , physics , geometry , quantum mechanics , nonlinear system , mechanical engineering , engineering
First, we prove that if the Reeb vector field $\xi$ of a Kenmotsu manifold $M$ leaves the Ricci operator $Q$ invariant, then $M$ is Einstein. Next, we study Kenmotsu manifold whose metric represents a Ricci soliton and prove that it is expanding. Moreover, the soliton is trivial (Einstein) if either (i) $V$ is a contact vector field, or (ii) the Reeb vector field $\xi$ leaves the scalar curvature invariant. Finally, it is shown that if the metric of a Kenmotsu manifold represents a gradient Ricci almost soliton, then it is $\eta$-Einstein and the soliton is expanding. We also exhibited some examples of Kenmotsu manifold that admit Ricci almost solitons.