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http://dx.doi.org/10.5666/KMJ.2021.61.3.645

3-Dimensional Trans-Sasakian Manifolds with Gradient Generalized Quasi-Yamabe and Quasi-Yamabe Metrics  

Siddiqi, Mohammed Danish (Department of Mathematics, Faculty of Science, Jazan University)
Chaubey, Sudhakar Kumar (Section of Mathematics, Department of Information Technology, University of Technology and Applied Sciences)
Ramandi, Ghodratallah Fasihi (Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University)
Publication Information
Kyungpook Mathematical Journal / v.61, no.3, 2021 , pp. 645-660 More about this Journal
Abstract
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 Poisson'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 manifold admits the gradient generalized almost quasi-Yamabe soliton with Hodge-de Rham potential ψ. This research ends with few examples of quasi-Yamabe solitons on 3-dimensional trans-Sasakian manifolds.
Keywords
gradient Generalized quasi-Yamabe soliton; quasi-Yamabe soliton; Trans-Sasakian manifold; Einstein manifold;
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