Spectral (isotropic) manifolds and their dimension

Abstract

A set of symmetric matrices whose ordered vector of eigenvalues belongs to a fixed set in Rn is called spectral or isotropic. In this paper, we establish that every locally symmetric submanifold M of Rn gives rise to a spectral manifold, for k ∈ {2, 3, . . . , ∞, ω}. An explicit formula for the dimension of the spectral manifold in terms of the dimension and the intrinsic properties of M is derived.