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Journal of Lie Theory, Vol. 11, No. 1, pp. 9-22 (2001)
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Reduction in contact geometry

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Frank Loose

Mathematisches Institut

der Universität

Auf der Morgenstelle 10

D-72076 Tübingen

frank.loose@uni-tuebingen.de

**Abstract:** The notion of a moment map for (exact) contact manifolds is introduced. We prove a reduction theorem analogous to the Marsden-Weinstein theorem in the (exact) symplectic case. Furthermore the existence of a local normal form for the moment map in a neighborhood of a point in the zero moment level is proved. This implies a local slice theorem for contact transformation groups.

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