On complete hypersurfaces of nonnegative sectional curvatures and constant 𝑚th mean curvature

Hartman, Philip

doi:10.1090/S0002-9947-1978-0511415-8

On complete hypersurfaces of nonnegative sectional curvatures and constant $m$th mean curvature
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Trans. Amer. Math. Soc. 245 (1978), 363-374 Request permission

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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Hypersurfaces with constant scalar curvature