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Triviality results for quasi k-Yamabe solitons

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Abstract

In this paper, we show that any compact quasi k-Yamabe gradient soliton must have constant \(\sigma _{k}\)-curvature. Moreover, we provide a certain condition for a compact quasi k-Yamabe soliton to be gradient, and for noncompact solitons, we present a geometric rigidity under a decay condition on the norm of the soliton field.

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Acknowledgements

The authors would like to thank the referee for his or her careful reading and valuable suggestions.

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Authors and Affiliations

  1. Universidade Federal do Acre, BR-364 km 4, 60440-Distrito Industrial, Rio Branco, AC, 69920-900, Brazil

    Willian Isao Tokura

  2. Instituto Federal do Tocantins, Rodovia TO-040, Km 349, Loteamento Rio Palmeira, Lote 01, Zona Rural, Dianópolis, TO, 77300-000, Brazil

    Elismar Dias Batista

  3. Universidade Federal de Goiás, INF, s/n, Goiânia, GO, 74690-900, Brazil

    Priscila Marques Kai

  4. Universidade Federal de Goiás, IME, 131 Goiânia, GO 74001-970, Brazil

    Marcelo Bezerra Barboza

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  1. Willian Isao Tokura
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  2. Elismar Dias Batista
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  3. Priscila Marques Kai
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  4. Marcelo Bezerra Barboza
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Correspondence to Willian Isao Tokura.

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Tokura, W.I., Batista, E.D., Kai, P.M. et al. Triviality results for quasi k-Yamabe solitons. Arch. Math. 119, 623–638 (2022). https://doi.org/10.1007/s00013-022-01795-1

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  • DOI: https://doi.org/10.1007/s00013-022-01795-1

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