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Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.

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Classification of "homogeneous" submanifolds of ℝⁿ

Such $M$ are called extrinsically homogeneous submanifolds of euclidean space. Reference: for example the book by Berndt-Console-Olmos, Submanifolds and holonomy. The set of all euclidean isometries t …
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