Pincement des sous-varietes extrinsequement homogenes dans un espace euclidien

Peter Quast

Pincement des sous-varietes extrinsequement homogenes dans un espace euclidien

Differential Geometry 2007-05-23 v2

Authors: Peter Quast

Abstract

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 $\R^m.$

Keywords

extrinsically homogeneous immersion closed manifold euclidean space almost metric connection tangent bundle normal bundle pinching parallel difference

Cite

@article{arxiv.math/0503271,
  title  = {Pincement des sous-varietes extrinsequement homogenes dans un espace euclidien},
  author = {Peter Quast},
  journal= {arXiv preprint arXiv:math/0503271},
  year   = {2007}
}

Comments

Detailed explications and proofs can be found in the article "Almost extriniscally homogeneous submanifolds of euclidean space" which will appear in the Journal "Annals of Global Analysis and Geometry"

Pincement des sous-varietes extrinsequement homogenes dans un espace euclidien

Abstract

Keywords

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