Types of submanifolds in symmetric spaces Sample Clauses

Types of submanifolds in symmetric spaces. Most types of submanifolds we are interested in follow a common pattern: they can be defined in more general Riemannian manifolds that are not necessarily symmetric, but they possess nice additional properties when the ambient space is symmetric. Perhaps, the most important such property that most of them acquire in the presence of symmetry is being homogeneous. 2.2.1. Let M be a Riemannian manifold. A complete submanifold S M is called (a) (extrinsically) homogeneous if it is an orbit of an isometric Lie group action on
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