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Yamabe and Quasi-Yamabe Solitons on Euclidean Submanifolds

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Abstract

In this paper, we initiate the study of Yamabe and quasi-Yamabe solitons on Euclidean submanifolds whose soliton fields are the tangential components of their position vector fields. Several fundamental results of such solitons were proved. In particular, we classify such Yamabe and quasi-Yamabe solitons on Euclidean hypersurfaces.

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Acknowledgements

This work is supported by King Saud University, Deanship of Scientific Research, College of Science Research Center.

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Authors and Affiliations

  1. Department of Mathematics, Michigan State University, 619 Red Cedar Road, East Lansing, MI, 48824–1027, USA

    Bang-Yen Chen

  2. Department of Mathematics, College of science, King Saud University, P.O. Box-2455, Riyadh, 11451, Saudi Arabia

    Sharief Deshmukh

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  1. Bang-Yen Chen
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  2. Sharief Deshmukh
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Correspondence to Bang-Yen Chen.

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Chen, BY., Deshmukh, S. Yamabe and Quasi-Yamabe Solitons on Euclidean Submanifolds. Mediterr. J. Math. 15, 194 (2018). https://doi.org/10.1007/s00009-018-1237-2

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  • DOI: https://doi.org/10.1007/s00009-018-1237-2

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