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Abstract: We study the varieties of invariant totally geodesic submanifolds ofisometries of the spherical, Euclidean and hyperbolic spaces in each finitedimension. We show that the dimensions of the connected components of thesevarieties determine the orbit type or the z-class of the isometry. For thispurpose, we introduce the Segre symbol of an isometry, a discrete invariantencoding the structure of its normal form, which parametrizes z-classes. Wethen provide a description of the isomorphism type of the varieties ofinvariant subspaces in terms of the Segre symbol.



Autor: Joana Cirici

Fuente: https://arxiv.org/







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