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A note on compact Weingarten hypersurfaces embedded in \(\mathbb {R}^{n + 1}\)

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Abstract

We prove that the round sphere is the only compact Weingarten hypersurface embedded in the Euclidean space such that \(H_r = aH + b\), for constants \(a, b \in \mathbb {R}\). Here, \(H_r\) stands for the r-th mean curvature and H denotes the standard mean curvature of the hypersurface.

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  1. Unidade Acadêmica de Ciências Exatas e da Natureza, Universidade Federal de Campina Grande, Cajazeiras, Paraíba, 58900-000, Brazil

    Eudes L. de Lima

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  1. Eudes L. de Lima
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Correspondence to Eudes L. de Lima.

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de Lima, E.L. A note on compact Weingarten hypersurfaces embedded in \(\mathbb {R}^{n + 1}\). Arch. Math. 111, 669–672 (2018). https://doi.org/10.1007/s00013-018-1233-6

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  • DOI: https://doi.org/10.1007/s00013-018-1233-6

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