On the structure of locally symmetric manifolds

Aris Danilidis (1, 2) , Jérôme Malick (3) , Hristo Sendov (4)

1 UAB - Departament de Matemàtiques [Barcelona]
2 DIM - Departamento de Ingeniería Matemática [Santiago]
3 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
4 Department of Statistics and Actuarial Science [Toronto]

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.

Mots clés: eigenvalue; Locally symmetric manifold; spectral manifold; permutation; partition; symmetric matrix

Domaines: Optimisation et contrôle [math.OC]; Géométrie différentielle [math.DG]

Aris Danilidis, Jérôme Malick, Hristo Sendov. On the structure of locally symmetric manifolds. [Research Report] LJK. 2014. ⟨hal-00972268⟩