A note on compact Weingarten hypersurfaces embedded in $$\mathbb {R}^{n + 1}$$ |
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Authors: | Eudes L de Lima |
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Institution: | 1.Unidade Acadêmica de Ciências Exatas e da Natureza,Universidade Federal de Campina Grande,Cajazeiras,Brazil |
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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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