Generalized K\"ahler structures on odd exact Courant algebroids

Vicente Cortes

Odd exact Courant algebroids form the simplest class of transitive Courant algebroids beyond the class of twisted generalized tangent bundles. Although their rank as vector bundles is odd, the notion of a generalized complex structure has been extended to that setting. I will define generalized Hermitian and generalized K\''ahler structures on odd exact Courant algebroids (allowing, both, definite and indefinite generalized metrics). Then I will describe these structures in terms of classical tensor fields on the base of the Courant algebroid. This is reminiscent of the bi-Hermitian viewpoint on generalized K\"ahler structures on exact Courant algebroids. Finally, I will discuss some classification results for left-invariant generalized K\''ahler structures on odd exact Courant algebroids over Lie groups of low dimensions. This talk is based on joint work with Liana David, see arXiv:2206.10456.

http://scgp.stonybrook.edu/video_portal/video.php?id=5868

Simons- Workshop: Supergravity, Generalized Geometry and Ricci Flow