Abstract
We derive a divergence formula for an m-quasi Yamabe gradient soliton with finite m, and use it to give a short proof of the result “A compact m-quasi Yamabe gradient soliton \((M^n,g)\), \(n\ge 3\), with finite m, has constant scalar curvature”. We also show that an m-quasi Yamabe gradient soliton with finite m and positive scalar curvature, whose soliton vector field leaves the Ricci tensor invariant, is shrinking and has constant scalar curvature.
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Acknowledgements
The authors are immensely thankful to the referee for his/her valuable suggestions towards the improvement of this paper. The first author was funded by the University Grants Commission (UGC), India, in the form of Senior Research Fellowship.
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Communicated by Mahuya Datta.
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Poddar, R., Sharma, R. & Subramanian, B. Notes on m-quasi Yamabe gradient solitons. Proc Math Sci 134, 2 (2024). https://doi.org/10.1007/s12044-024-00775-5
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DOI: https://doi.org/10.1007/s12044-024-00775-5