Pincement des sous-varietes extrinsequement homogenes dans un espace euclidien

Abstract

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

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"