Integrability of generalized structures on odd exact Courant algebroids using generalized connections
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918509236191232 |
|---|---|
| author | Cortés, Vicente David, Liana Mirea, Marius |
| author_facet | Cortés, Vicente David, Liana Mirea, Marius |
| contents | Odd exact Courant algebroids constitute a simple class of transitive Courant algebroids. Their underlying vector bundle is of odd rank and differs from a generalized tangent bundle by the addition of a line bundle. In this article we study natural analogues of almost complex and almost pseudo-Hermitian structures on such Courant algebroids, which are called B_n-generalized almost complex/pseudo-Hermitian structures. The corresponding integrable structures are known as B_n-generalized complex structures and B_n-generalized pseudo-Kähler structures, respectively. We characterize the integrability of B_n-generalized almost complex/pseudo-Hermitian structures on odd exact Courant algebroids in terms of existence of adapted generalized connections. We describe the affine spaces of adapted generalized connections for such integrable generalized structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18306 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Integrability of generalized structures on odd exact Courant algebroids using generalized connections Cortés, Vicente David, Liana Mirea, Marius Differential Geometry Odd exact Courant algebroids constitute a simple class of transitive Courant algebroids. Their underlying vector bundle is of odd rank and differs from a generalized tangent bundle by the addition of a line bundle. In this article we study natural analogues of almost complex and almost pseudo-Hermitian structures on such Courant algebroids, which are called B_n-generalized almost complex/pseudo-Hermitian structures. The corresponding integrable structures are known as B_n-generalized complex structures and B_n-generalized pseudo-Kähler structures, respectively. We characterize the integrability of B_n-generalized almost complex/pseudo-Hermitian structures on odd exact Courant algebroids in terms of existence of adapted generalized connections. We describe the affine spaces of adapted generalized connections for such integrable generalized structures. |
| title | Integrability of generalized structures on odd exact Courant algebroids using generalized connections |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2605.18306 |