1Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany 2The 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. 3[
Journal of Lie Theory, Tome 11 (2001) no. 1, pp. 9-22
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Frank Loose. Reduction in Contact Geometry. Journal of Lie Theory, Tome 11 (2001) no. 1, pp. 9-22. http://geodesic.mathdoc.fr/item/JOLT_2001_11_1_a1/
@article{JOLT_2001_11_1_a1,
author = {Frank Loose},
title = {Reduction in {Contact} {Geometry}},
journal = {Journal of Lie Theory},
pages = {9--22},
year = {2001},
volume = {11},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2001_11_1_a1/}
}
TY - JOUR
AU - Frank Loose
TI - Reduction in Contact Geometry
JO - Journal of Lie Theory
PY - 2001
SP - 9
EP - 22
VL - 11
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2001_11_1_a1/
ID - JOLT_2001_11_1_a1
ER -
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%A Frank Loose
%T Reduction in Contact Geometry
%J Journal of Lie Theory
%D 2001
%P 9-22
%V 11
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2001_11_1_a1/
%F JOLT_2001_11_1_a1
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.
