TY - JOUR
T1 - Reduction of generalized complex structures
AU - Stiénon, Mathieu
AU - Xu, Ping
N1 - Funding Information:
Ping Xu would like to thank the Université Pierre et Marie Curie, Paris , for hospitality while work on this project was being done. We would like to thank Henrique Bursztyn, Camille Laurent-Gengoux, Aissa Wade and Alan Weinstein for many useful discussions. Special thanks go to Tudor Ratiu, who kindly called our attention to many references on related subjects that we overlooked in an earlier version. Finally, we thank the organizers of the conference “Poisson geometry” - Trieste, July 2005 , for having given us the chance to present this work. The second author’s research was partially supported by NSF grant DMS03-06665 and NSA grant 03G-142.
PY - 2008/1
Y1 - 2008/1
N2 - We study reduction of generalized complex structures. More precisely, we investigate the following question. Let J be a generalized complex structure on a manifold M, which admits an action of a Lie group G preserving J. Assume that M0 is a G-invariant smooth submanifold and the G-action on M0 is proper and free so that MG {colon equals} M0 / G is a smooth manifold. Under what condition does J descend to a generalized complex structure on MG? We describe a sufficient condition for the reduction to hold, which includes the Marsden-Weinstein reduction of symplectic manifolds and the reduction of the complex structures in Kähler manifolds as special cases. As an application, we study reduction of generalized Kähler manifolds.
AB - We study reduction of generalized complex structures. More precisely, we investigate the following question. Let J be a generalized complex structure on a manifold M, which admits an action of a Lie group G preserving J. Assume that M0 is a G-invariant smooth submanifold and the G-action on M0 is proper and free so that MG {colon equals} M0 / G is a smooth manifold. Under what condition does J descend to a generalized complex structure on MG? We describe a sufficient condition for the reduction to hold, which includes the Marsden-Weinstein reduction of symplectic manifolds and the reduction of the complex structures in Kähler manifolds as special cases. As an application, we study reduction of generalized Kähler manifolds.
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U2 - 10.1016/j.geomphys.2007.09.009
DO - 10.1016/j.geomphys.2007.09.009
M3 - Article
AN - SCOPUS:37349123888
SN - 0393-0440
VL - 58
SP - 105
EP - 121
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
IS - 1
ER -