Spectral (isotropic) manifolds and their dimension

© 2016, Hebrew University Magnes Press. A set of n × n 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 Ck submanifoldMof ℝn gives rise to a Ck 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. This work builds upon the results of Sylvester and Šilhavý and uses characteristic properties of locally symmetric submanifolds established in recent works by the authors.