Orbit types of isometries of spaces of constant curvature and invariant subspaces

Details Orbit types of isometries of spaces of constant curvature and invariant subspaces Orbit types of isometries of spaces of constant curvature and invariant subspaces

2009-04-27

arxiv.org/abs/0904.4141v1

Mathematics

Differential Geometry

Scientific paper

We study the orbit types of isometries of the spherical, Euclidean and hyperbolic spaces in each finite dimension, and show that they are parameterized by a discrete algebraic invariant, the Segre symbol. In particular, we prove that the number of orbit types is finite. We study the varieties of invariant totally geodesic submanifolds of an isometry, and show that the dimensions of the connected components of these varieties determine the Segre symbol of the isometry, and thus its orbit type.

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