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Abstract |
Path geometry and CR structures on real 3-manifolds were studied by E. Cartan. There is an interesting local geometry with curvature invariants and an interesting global geometry. In particular, one can obtain flat structures studying configurations of flags. The model spaces are closed orbits of SL(3,R) and SU(2,1) in a complex flag manifold. We will review these geometries and discuss a notion of flag structure, which includes both geometries. We also review volume and Chern-Simons invariants for such geometric structures. |
