外在对称子空间

Pub Date : 2020-07-01 DOI:10.18910/76678

J. Eschenburg, M. Tanaka

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引用次数: 0

摘要

外对称空间是一个子流形M⊂V=Rn，它通过沿每个法线空间NxM的反射sx保持不变。一个外对称子空间是某个子空间V′⊂V的交集MåV′的连通分量M′，它对任何x∈M′都是sx不变的。我们给出了所有这样的子空间V′的代数性质。

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Extrinsic symmetric subspaces

An extrinsic symmetric space is a submanifold M ⊂ V = Rn which is kept invariant by the reflection sx along every normal space NxM. An extrinsic symmetric subspace is a connected component M′ of the intersection M ∩ V ′ for some subspace V ′ ⊂ V which is sx-invariant for any x ∈ M′. We give an algebraic charactrization of all such subspaces V ′.

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