Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2019; 34(1): 321-331

Online first article June 28, 2018      Printed January 31, 2019

https://doi.org/10.4134/CKMS.c180060

Copyright © The Korean Mathematical Society.

Yamabe solitons on Kenmotsu manifolds

Shyamal Kumar Hui, Yadab Chandra Mandal

The University of Burdwan; The University of Burdwan

Abstract

The present paper deals with a study of infinitesimal $CL$-transformations on Kenmotsu manifolds, whose metric is Yamabe soliton and obtained sufficient conditions for such solitons to be expanding, steady and shrinking. Among others, we find a necessary and sufficient condition of a Yamabe soliton on Kenmotsu manifold with respect to $CL$-connection to be Yamabe soliton on Kenmotsu manifold with respect to Levi-Civita connection. We found the necessary and sufficient condition for the Yamabe soliton structure to be invariant under Schouten-Van Kampen connection. Finally, we constructed an example of steady Yamabe soliton on $3$-dimensional Kenmotsu manifolds with respect to Schouten-Van Kampen connection.

Keywords: Yamabe soliton, Kenmotsu manifold, infinitesimal $CL$-trans\-formation, Schouten-Van Kampen connection

MSC numbers: 53C15, 53C25, 53B05