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Almost Extrinsically Homogeneous Submanifolds of Euclidean Space

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Abstract

Consider a closed manifold M immersed in Rm. Suppose that the trivial bundle M × Rm = T M ⊗ ν M is equipped with an almost metric connection ~ ∇ which almost preserves the decomposition of M × Rm into the tangent and the normal bundle. Assume moreover that the difference Γ = ∂~∇ with the usual derivative ∂ in Rm is almost ~∇-parallel. Then M admits an extrinsically homogeneous immersion into Rm.

Mathematics Subject Classifications (2000): 53C20, 53C24, 53C30, 53C42, 53C40.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Augsburg, 86159, Augsburg, Germany

    Peter Quast

  2. Département de mathématiques, Université de Fribourg, 1700, Fribourg, Switzerland

    Peter Quast

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  1. Peter Quast
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Correspondence to Peter Quast.

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Quast, P. Almost Extrinsically Homogeneous Submanifolds of Euclidean Space. Ann Glob Anal Geom 29, 1–16 (2006). https://doi.org/10.1007/s10455-006-7278-y

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  • DOI: https://doi.org/10.1007/s10455-006-7278-y

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