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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| Affiliation: | 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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