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On complete hypersurfaces of nonnegative sectional curvatures and constant $ m$th mean curvature


Author: Philip Hartman
Journal: Trans. Amer. Math. Soc. 245 (1978), 363-374
MSC: Primary 53C45
DOI: https://doi.org/10.1090/S0002-9947-1978-0511415-8
MathSciNet review: 511415
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Abstract: The main result is that if $ M = {M^n}$ is a complete Riemann manifold of nonnegative sectional curvature and $ X:\,M \to {R^{n + 1}}$ is an isometric immersion such that $ X(M)$ has a positive constant mth mean curvature, then $ X(M)$ is the product of a Euclidean space $ {R^{n - d}}$ and a d-dimensional sphere, $ m \leqslant d \leqslant n$.


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DOI: https://doi.org/10.1090/S0002-9947-1978-0511415-8
Article copyright: © Copyright 1978 American Mathematical Society

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