Pincement des sous-varietes extrinsequement homogenes dans un espace euclidien

2005/03/14 by Peter Quast, Quast, Peter
Mathematics · #53C20 #53C24 #53C30 #53C40 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:53C20 #msc:53C24 #msc:53C30 #msc:53C40 #msc:53C42

paper · pdf · doi:10.48550/arxiv.math/0503271

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"

openalex publication_date 2005/03/14 · arxiv created 2005/06/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider a closed manifold M immersed in \R^m. Suppose that the trivial bundle M×\R^m=TM⊗ νM is equipped with an almost metric connection ∇ which almost preserves the decomposition of M×\R^m into the tangent and the normal bundle. Assume moreover that the difference Γ=∂-∇ with the usual derivative ∂ in \R^m is almost ∇-parallel. We show that under these assumptions M admits an extrinsically homogeneous immersion into \R^m.

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