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Some characterizations of quasi Yamabe solitons

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Abstract

In this article, we have proved some results in connection with the potential vector field having finite global norm in quasi Yamabe soliton. We have derived some criteria for the potential vector field on the non-positive Ricci curvature of the quasi Yamabe soliton. Also, a necessary condition for a compact quasi Yamabe soliton has been formulated. We further showed that if the potential vector field has a finite global norm in a complete non-trivial, non-compact quasi Yamabe soliton with finite volume, then the scalar curvature becomes constant and the soliton reduces to a Yamabe soliton.

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Acknowledgements

The authors convey their sincere thanks and gratitude to the referee for the valuable suggestions towards the improvement of the paper. The second author gratefully acknowledges to the CSIR(File No.:09/025(0282)/2019-EMR-I), Govt. of India for the award of JRF.

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  1. Department of Mathematics, University of Burdwan, Golapbag, Burdwan, West Bengal, 713104, India

    Absos Ali Shaikh & Prosenjit Mandal

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  1. Absos Ali Shaikh
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  2. Prosenjit Mandal
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Correspondence to Absos Ali Shaikh.

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Shaikh, A.A., Mandal, P. Some characterizations of quasi Yamabe solitons. J. Geom. 114, 3 (2023). https://doi.org/10.1007/s00022-022-00664-0

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