Abstract
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 C k submanifoldMof ℝn gives rise to a C k 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.
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Research supported by the grant MTM2014-59179-C2-1-P (MINECO of Spain and FEDER of EU), by the BASAL Project PFB-03, and by the FONDECYT Regular grant No 1130176 (Chile).
Research supported by the NSERC of Canada.
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Daniilidis, A., Malick, J. & Sendov, H. Spectral (isotropic) manifolds and their dimension. JAMA 128, 369–397 (2016). https://doi.org/10.1007/s11854-016-0013-0
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DOI: https://doi.org/10.1007/s11854-016-0013-0