Displaying similar documents to “Geometry of Submanifolds. I. The first Casorati curvature indicatrices”

Universal natural shapes

Johan Gielis, Stefan Haesen, Leopold Verstraelen (2005)

Kragujevac Journal of Mathematics

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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 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 ) .

On an inequality of Oprea for Lagrangian submanifolds

Franki Dillen, Johan Fastenakels (2009)

Open Mathematics

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We show that a Lagrangian submanifold of a complex space form attaining equality in the inequality obtained by Oprea in [8], must be totally geodesic.

Some contributions to the differential geometry of submanifolds

Barbara Opozda

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CONTENTSI. 1. Introduction..................................................................................................................................................................5   2. Preliminaries..............................................................................................................................................................11   3. On Simon’s conjecture..............................................................................................................................................13II....

Willmore submanifolds in the unit sphere.

Guo Zhen (2004)

Collectanea Mathematica

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In this paper we generalize the self-adjoint differential operator (used by Cheng-Yau) on hypersurfaces of a constant curvature manifold to general submanifolds. The generalized operator is no longer self-adjoint. However we present its adjoint operator. By using this operator we get the pinching theorem on Willmore submanifolds which is analogous to the pinching theorem on minimal submanifold of a sphere given by Simon and Chern-Do Carmo-Kobayashi.