STUDY OF RICCI SOLITONS IN f-KENMOTSU MANIFOLDS WITH THE QUARTER-SYMMETRIC METRIC CONNECTION
By
N. V. C. Shukla and Amisha Sharma
Department of Mathematics and Astronomy, University of Lucknow,Lucknow, Uttar Pradesh,India-226007
Email: nvcshukla72@gmail.com, amishasharma966@gmail.com
(Received: September 28, 2022; In format: October 31, 2023; Revised: May 16, 2023; Accepted : May 17, 2023)
DOI: https://doi.org/10.58250/jnanabha.2023.53135
Abstract
In this paper, the non-existence of ξ-projectively flat 3-dimensional f -Kenmotsu manifold with quarter-symmetric metric connection has been established. Moreover, we prove that 3-dimensional f - Kenmotsu manifold with the quarter-symmetric metric connection is an η- Einstein manifold and the Ricci soliton is given as expanding or shrinking under certain restrictions on f .
2020 Mathematical Sciences Classification: 53C15, 53C20
Keywords and Phrases: Kenmotsu manifold, Ricci solitons, Quarter-symmetric metric connection.