A canonical reductive decomposition is constructed for extrinsic homogeneous submanifolds of homogeneous Riemannian manifolds, derived from any reductive decomposition of the ambient space.
Almost extrinsically homogeneous submanifolds of Euclidean space
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Canonical Reductive Decomposition of Extrinsic Homogeneous Submanifolds
A canonical reductive decomposition is constructed for extrinsic homogeneous submanifolds of homogeneous Riemannian manifolds, derived from any reductive decomposition of the ambient space.