Article
Kyungpook Mathematical Journal 2021; 61(3): 645-660
Published online September 30, 2021
Copyright © Kyungpook Mathematical Journal.
3-Dimensional Trans-Sasakian Manifolds with Gradient Generalized Quasi-Yamabe and Quasi-Yamabe Metrics
Mohammed Danish Siddiqi, Sudhakar Kumar Chaubey, Ghodratallah Fasihi Ramandi*
Department of Mathematics, Faculty of Science, Jazan University, Jazan, Kingdom of Saudi Arabia
e-mail : msiddiqi@jazanu.edu.sa
Section of Mathematics, Department of Information Technology, University of Technology and Applied Sciences, Shinas, P. O. box 77, Postal Code 324, Oman
e-mail : sudhakar.chaubey@shct.edu.om
Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran
e-mail : fasihi@sci.ikiu.ac.ir
Received: January 25, 2021; Revised: June 21, 2021; Accepted: July 6, 2021
This paper examines the behavior of a 3-dimensional trans-Sasakian manifold equipped with a gradient generalized quasi-Yamabe soliton. In particular, It is shown that α-Sasakian, β-Kenmotsu and cosymplectic manifolds satisfy the gradient generalized quasi-Yamabe soliton equation. Furthermore, in the particular case when the potential vector field ζ of the quasi-Yamabe soliton is of gradient type ζ = grad(ψ), we derive a Pois-son’s equation from the quasi-Yamabe soliton equation. Also, we study harmonic aspects of quasi-Yamabe solitons on 3-dimensional trans-Sasakian manifolds sharing a harmonic potential function ψ. Finally, we observe that 3-dimensional compact trans-Sasakian mani-fold admits the gradient generalized almost quasi-Yamabe soliton with Hodge-de Rham po-tential ψ. This research ends with few examples of quasi-Yamabe solitons on 3-dimensional trans-Sasakian manifolds.