Almost Extrinsically Homogeneous Submanifolds of Euclidean Space |
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Authors: | Peter Quast |
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Affiliation: | 1. Institut für Mathematik, Universit?t Augsburg, 86159, Augsburg, Germany 2. Département de mathématiques, Université de Fribourg, 1700, Fribourg, Switzerland
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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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Keywords: | submanifolds extrinsic geometry homogeneity pinching orbits |
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