Dirac and Generalized Complex Structures on Cartan Geometries

2012/04/26 by Honglei Lang, Xiaomeng Xu, Lang, Honglei +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.DG

paper · pdf · doi:10.48550/arxiv.1204.5951

12 pages

openalex publication_date 2012/04/26 · arxiv created 2012/06/24 · arxiv updated 2012/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce linear Dirac and generalized complex structures on Cartan geometries and give criteria for Dirac subalgebras of \frkg\ltimes\frkg^* representing Dirac structures on a Cartan geometry. We prove that there is a bijection between the linear generalized structures on a torsion free Cartan geometry and the equivariant generalized structures on its corresponding homogeneous space.

Citations

• Note on pre-Courant algebroid structures for parabolic geometries
• Generalized Complex and Dirac Structures on Homogeneous Spaces
• Generalized Complex Geometry

Related

• Dirac structures on generalized Riemannian manifolds
• Two Categories of Dirac Manifolds
• Generalized Complex and Dirac Structures on Homogeneous Spaces
• Dirac structures for generalized Courant and Courant algebroids
• An introduction to Cartan geometries