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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Curvature Pinching and Eigenvalue Rigidity for Minimal Submanifolds.

Sebastián Montiel, A. Ros, F. Urbano (1986)

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Slant submanifolds with prescribed scalar curvature into cosymplectic space form.

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Curvature estimate for the volume growth of globally minimal submanifolds.

Le Hong Van (1993)

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

Shichang, Shu, Sanyang, Liu (2004)

Balkan Journal of Geometry and its Applications (BJGA)

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On total curvature of immersions and minimal submanifolds of spheres

Giovanni Rotondaro (1993)

Commentationes Mathematicae Universitatis Carolinae

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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.

Li, Haizhong (1996)

Bulletin of the Belgian Mathematical Society - Simon Stevin

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A pointwise inequality in submanifold theory

P. J. De Smet, F. Dillen, Leopold C. A. Verstraelen, L. Vrancken (1999)

Archivum Mathematicum

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We obtain a pointwise inequality valid for all submanifolds $M^{n}$ of all real space forms $N^{n + 2} (c)$ with $n \geq 2$ and with codimension two, relating its main scalar invariants, namely, its scalar curvature from the intrinsic geometry of $M^{n}$ , and its squared mean curvature and its scalar normal curvature from the extrinsic geometry of $M^{n}$ in $N^{m} (c)$ .

A note on the first Betti number of submanifolds with nonnegative Ricci curvature in codimension two.

Maria Helena Noronha (1991)

Manuscripta mathematica

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