EUDML | On total curvature of immersions and minimal submanifolds of spheres

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Displaying similar documents to “On total curvature of immersions and minimal submanifolds of spheres”

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 $N^{m} (c)$ .

Global pinching theorems of submanifolds in spheres.

Cai, Kairen (2002)

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

Li, Haizhong (1993)

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Submanifolds of Euclidean space with parallel mean curvature vector.

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Slant submanifolds with prescribed scalar curvature into cosymplectic space form.

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Balkan Journal of Geometry and its Applications (BJGA)

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Topology and geometry of complete submanifolds in euclidean spaces

Qing-Ming Cheng (2005)

Banach Center Publications

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This paper is a survey of results on topological structures and curvature structures of complete submanifolds in a Euclidean space.