Reduction of generalized complex structures

JOURNAL OF GEOMETRY AND PHYSICS

卷:58

Article; Proceedings Paper

Stienon, Mathieu¹  Xu, Ping¹ 

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

关键词: Courant algebroids;    Dirac structures;    Lie algebroids;    Lie bialgebroids;    Poisson geometry;    symplectic reduction;   

DOI  :  10.1016/j.geomphys.2007.09.009

来源: Elsevier

【 摘 要 】

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 M-0 is a G-invariant smooth submanifold and the G-action on M-0 is proper and free so that M-G := M-0/G is a smooth manifold. Under what condition does J descend to a generalized complex structure on M-G? 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 Kahler manifolds as special cases. As an application, we study reduction of generalized Kahler manifolds. (C) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

Free