Extrinsic symmetric subspaces

Abstract

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 ′.