Symmetries of parabolic contact structures

Details Symmetries of parabolic contact structures Symmetries of parabolic contact structures

2010-03-29

arxiv.org/abs/1003.5443v1

Journal of Geometry and Physics, Volume 60, Issue 11, November 2010,1698-1709

Mathematics

Differential Geometry

19 pages

Scientific paper

10.1016/j.geomphys.2010.06.013

We generalize the concept of locally symmetric spaces to parabolic contact structures. We show that symmetric normal parabolic contact structures are torsion--free and some types of them have to be locally flat. We prove that each symmetry given at a point with non--zero harmonic curvature is involutive. Finally we give restrictions on number of different symmetries which can exist at such a point.

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