Reduction of Courant algebroids and generalized complex structures

被引：135

作者：

Bursztyn, Henrique

Cavalcanti, Gil R.

Gualtieri, Marco ^{[1
]}

机构：

[1] MIT, Dept Math, 77 Massachusetts Ave, Cambridge, MA 02139 USA

[2] Math Inst, Oxford OX1 3LB, England

[3] Inst Matematica Pura & Aplicada, BR-22460320 Rio De Janeiro, Brazil

来源：

ADVANCES IN MATHEMATICS | 2007年 / 211卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

reduction; Courant algebroid; Dirac structure; generalized complex geometry; Bi-Hermitian structure; DIRAC STRUCTURES; HOMOGENEOUS SPACES; LIE-ALGEBRAS; MANIFOLDS;

D O I：

10.1016/j.aim.2006.09.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a theory of reduction for Courant algebroids as well as Dirac structures, generalized complex, and generalized Kahler structures which interpolates between holomorphic reduction of complex manifolds and symplectic reduction. The enhanced symmetry group of a Courant algebroid leads us to define extended actions and a generalized notion of moment map. Key examples of generalized Kahler reduced spaces include new explicit bi-Hermitian metrics on CP2. (C) 2006 Elsevier Inc. All rights reserved.

引用

页码：726 / 765

页数：40

共 32 条

[1]

[Anonymous], 1974, Reports on Mathematical Physics, V5, P121, DOI 10.1016/0034-4877(74)90021-4

[2]

BAEZ J, MATHQA0307263

[3] Symmetry and reduction in implicit generalized Hamiltonian systems [J].