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

  • 투고 : 2021.01.25
  • 심사 : 2021.07.06
  • 발행 : 2021.09.30

초록

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.

키워드

과제정보

The authors express their sincere thanks to the anonymous referees for the valuable suggestions and comments for the improvement of the paper.

참고문헌

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