Almost Extrinsically Homogeneous Submanifolds of Euclidean Space

Quast, Peter

In: Annals of Global Analysis and Geometry, 2006, vol. 29, no. 1, p. 1-16

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    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