Pincement des sous-varietes extrinsequement homogenes dans un espace euclidien
Abstract
Description
Consider a closed manifold $M$ immersed in $\R^m.$ Suppose that the trivial bundle $M\times\R^m=TM\otimes νM$ 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 $Γ=\partial-\tilde{\nabla}$ 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 $\R^m.$
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"
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"