2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74487Consider 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"Differential Geometry53C20; 53C24; 53C30; 53C42; 53C40text