On the structure of locally symmetric manifolds
Résumé
This paper studies structural properties of locally symmetric submanifolds. One of the main result states that a locally symmetric submanifold M of Rn admits a locally symmetric tangential parametrization in an appropriately reduced ambient space. This property has its own interest and is the key element to establish that the spectral set consisting of all symmetric matrices having their eigenvalues on M, is a smooth submanifold of the space of symmetric matrices Sn.
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