On Complete Hypersurfaces of Nonnegative Sectional Curvatures and Constant mth Mean Curvatures
Copyright policy )On Complete Hypersurfaces of Nonnegative Sectional Curvatures and Constant mth Mean Curvatures
The main result is that if M = M n M = {M^n} is a complete Riemann manifold of nonnegative sectional curvature and X : M → R n + 1 X:\,M \to {R^{n + 1}} is an isometric immersion such that X ( M ) X(M) has a positive constant mth mean curvature, then X ( M ) X(M) is the product of a Euclidean space R n − d {R^{n - d}} and a d-dimensional sphere, m ⩽ d ⩽ n m \leqslant d \leqslant n .
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), second fundamental form, Global submanifolds, mean curvature, nonnegative sectional curvatures, Elliptic equations and elliptic systems, complete hypersurfaces
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), second fundamental form, Global submanifolds, mean curvature, nonnegative sectional curvatures, Elliptic equations and elliptic systems, complete hypersurfaces
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