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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.21881 |
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| _version_ | 1866911272446984192 |
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| author | Cavalcanti, Gil R. Pedregal, Jaime Rubio, Roberto |
| author_facet | Cavalcanti, Gil R. Pedregal, Jaime Rubio, Roberto |
| contents | We consider a family of metric generalized connections on transitive Courant algebroids, which includes the canonical Levi-Civita connection, and study the flatness condition. We find that the building blocks for such flat transitive Courant algebroids are compact simple Lie groups. Further, we give a description of left-invariant flat Levi-Civita generalized connections on such Lie groups, which, in particular, shows the existence of non-flat ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21881 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Flat Generalized Connections on Courant Algebroids Cavalcanti, Gil R. Pedregal, Jaime Rubio, Roberto Differential Geometry We consider a family of metric generalized connections on transitive Courant algebroids, which includes the canonical Levi-Civita connection, and study the flatness condition. We find that the building blocks for such flat transitive Courant algebroids are compact simple Lie groups. Further, we give a description of left-invariant flat Levi-Civita generalized connections on such Lie groups, which, in particular, shows the existence of non-flat ones. |
| title | Flat Generalized Connections on Courant Algebroids |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2503.21881 |