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Compact Lorentz 3-folds with non-compact isometry groups.

It is a well known phenomenon that compact Lorentz-manifolds may admit a non-compact isometry group. The most readily accessible example is that of a flat Lorentz torus \(\mathbb{T}^n = \mathbb{M}^n/\mathbb{Z}^n\), the quotient of Minkowski space by integer translations, here the isometry group is \(O(n − 1, 1)_{\mathbb{Z}} \ltimes \mathbb{T}^n\). In [Fr 18] C. Frances provides a complete classification of all compact Lorentz 3-folds with non-compact isometry groups. Throughout [Fr 18] the language of Cartan geometries is used, and many of the initial steps, which show that such a manifold must admit many local Killing fields, are valid in this general setting. This thesis reviews this proof and provides an introduction to the theory of Cartan connections.

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Year: 2019

Author : Oskar Riedler

Prof. Dr. Beatrice Pozzetti