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Some half-space theorems in the real projective space

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Abstract

In this paper, under certain conditions on the mean and scalar curvatures, we prove that there are no strongly stable linear Weingarten closed two-sided hypersurfaces immersed in a certain region determined by a geodesic sphere of the \((n+1)\)-dimensional real projective space \(\mathbb{R}\mathbb{P}^{n+1}\). We also provide a rigidity result for these hypersurfaces.

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Acknowledgements

The authors would like to thank the referee for his/her valuable suggestions and useful comments which improved the paper.

Funding

The first author is partially supported by CNPq, Brazil, grant 304891/2021-5. The second author is partially supported by CNPq, Brazil, grant 301970/2019-0.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Campina Grande, Campina Grande, Paraíba, 58.429-970, Brazil

    Marco A. L. Velásquez, Henrique F. de Lima & José H. H. de Lacerda

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  1. Marco A. L. Velásquez
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  2. Henrique F. de Lima
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  3. José H. H. de Lacerda
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Correspondence to Marco A. L. Velásquez.

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Communicated by Davi Maximo.

Dedicated to Manfredo P. do Carmo, in memory.

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Velásquez, M.A.L., de Lima, H.F. & de Lacerda, J.H.H. Some half-space theorems in the real projective space. São Paulo J. Math. Sci. 17, 595–614 (2023). https://doi.org/10.1007/s40863-023-00371-x

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