Pincement des sous-varietes extrinsequement homogenes dans un espace euclidien

Details Pincement des sous-varietes extrinsequement homogenes dans un espace euclidien Pincement des sous-varietes extrinsequement homogenes dans un espace euclidien

2005-03-14

arxiv.org/abs/math/0503271v2

Mathematics

Differential Geometry

Detailed explications and proofs can be found in the article "Almost extriniscally homogeneous submanifolds of euclidean space

Scientific paper

Consider a closed manifold $M$ immersed in $\R^m.$ Suppose that the trivial bundle $M\times\R^m=TM\otimes \nu M$ is equipped with an almost metric connection $\tilde{\nabla}$ which almost preserves the decomposition of $M\times\R^m$ into the tangent and the normal bundle. Assume moreover that the difference $\Gamma=\partial-\tilde{\nabla}$ with the usual derivative $\partial$ in $\R^m$ is almost $\tilde{\nabla}$-parallel. We show that under these assumptions $M$ admits an extrinsically homogeneous immersion into $\R^m.$

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