A two-dimensional surface with everywhere positive curvature is a closed surface with no boundary (isomprphic to a sphere).(adsbygoogle = window.adsbygoogle || []).push({});

Is this true for higher dimensional surfaces as well?

Would a three-dimensional surface, with everywhere positive curvature be a closed hypersurface isomorphic to a hypersphere?

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# Curvature implying Closedness in N dimensions

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