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.

34 pages. To appear in Selecta Mathematica, New Series

References in corpus (10)

• A Gradient Flow for Worldsheet Nonlinear Sigma Models
• Torsion-free generalized connections and Heterotic Supergravity
• Symmetries in generalized Kähler geometry
• Infinitesimal moduli for the Strominger system and Killing spinors in generalized geometry
• On Regular Courant Algebroids
• Ricci flow, Courant algebroids, and renormalization of Poisson--Lie T-duality
• Formality in generalized Kahler geometry
• Scalar curvature as moment map in generalized Kahler geometry
• Palatini Variation in Generalized Geometry and String Effective Actions
• On the Equivalence of Generalized Ricci Curvatures