Mathematics – Differential Geometry
Scientific paper
2008-10-15
Geom. Dedicata 146, 1 (2010) 67-83
Mathematics
Differential Geometry
AMSLaTeX, 16 pages
Scientific paper
10.1007/s10711-009-9426-6
Contact projective structures have been profoundly studied by D.J.F. Fox. He associated to a contact projective structure a canonical projective structure on the same manifold. We interpret Fox' construction in terms of the equivalent parabolic (Cartan) geometries, showing that it is an analog of Fefferman's construction of a conformal structure associated to a CR structure. We show that, on the level of Cartan connections, this Fefferman--type construction is compatible with normality if and only if the initial structure has vanishing contact torsion. This leads to a geometric description of the paths that have to be added to the contact geodesics of a contact projective structure in order to obtain the subordinate projective structure. They are exactly the chains associated to the contact projective structure, which are analogs of the Chern-Moser chains in CR geometry. Finally, we analyze the consequences for the geometry of chains and prove that a chain-preserving contactomorphism must be a morphism of contact projective structures.
Cap Andreas
Zadnik Vojtech
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