Reduction of generalized complex structures |
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Authors: | Mathieu Stiénon Ping Xu |
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Institution: | Department of Mathematics, Pennsylvania State University, University Park, PA 16802, United States |
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Abstract: | 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?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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Keywords: | 53D17 53D20 |
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