Flat Generalized Connections on Courant Algebroids
Abstract 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.
Authors
- Gil R. Cavalcanti (ORCID: https://orcid.org/0000-0002-4089-7460)
- Roberto Rubio (ORCID: https://orcid.org/0000-0003-1645-1722)
- Jaime Pedregal
Institutions
- Universitat Autònoma de Barcelona (ES)
- Utrecht University (NL)
Publication Details
- Journal
- Selecta Mathematica
- Published
- 2025-09-01
- DOI
- https://doi.org/10.1007/s00029-025-01083-0
- Primary Topic
- Homotopy and Cohomology in Algebraic Topology
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek
- Ministerio de Ciencia e Innovación
- Agència de Gestió d'Ajuts Universitaris i de Recerca
- Agencia Estatal de Investigación