Curvature pinching for odd-dimensional minimal submanifolds in a sphere.

Li, Haizhong

Displaying similar documents to “Curvature pinching for odd-dimensional minimal submanifolds in a sphere.”

Curvature Pinching for Odd-dimensional Minimal Submanifolds in a Sphere

Li Haizhong (1993)

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Complete space-like submanifolds with constant scalar curvature in a de Sitter space.

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On total curvature of immersions and minimal submanifolds of spheres

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For closed immersed submanifolds of Euclidean spaces, we prove that ${\int | μ |}^{2} d V \geq V / R^{2}$ , where $μ$ is the mean curvature field, $V$ the volume of the given submanifold and $R$ is the radius of the smallest sphere enclosing the submanifold. Moreover, we prove that the equality holds only for minimal submanifolds of this sphere.

The Ricci curvature of totally real 3-dimensional submanifolds of the nearly Kaehler 6-sphere.

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