Prehomogeneous Affine Representations and Flat Pseudo-Riemannian Manifolds

Details Prehomogeneous Affine Representations and Flat Pseudo-Riemannian Manifolds Prehomogeneous Affine Representations and Flat Pseudo-Riemannian Manifolds

2008-09-04

arxiv.org/abs/0809.0824v1

Mathematics

Differential Geometry

Scientific paper

The theory of flat Pseudo-Riemannian manifolds and flat affine manifolds is closely connected to the topic of prehomogeneous affine representations of Lie groups. In this article, we exhibit several aspects of this correspondence. At the heart of our presentation is a development of the theory of characteristic classes and characters of prehomogeneous affine representations. We give applications concerning flat affine, as well as Pseudo-Riemannian and symplectic affine flat manifolds.

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