On generalized Kähler geometry on compact Lie groups

Abstract

We present some fundamental facts about a class of generalized Kähler structures defined by invariant complex structures on compact Lie groups. The main computational tool is the BH-to-GK spectral sequences that relate the bi-Hermitian data to generalized geometry data. The relationship between generalized Hodge decomposition and generalized canonical bundles for generalized Kähler manifolds is also clarified.

Differential calculus for generalized geometry and geometric Lax flows

“…Functionals involving curvatures, such as the Yang-Mills functional, can be extended ( §3.3) and lead to natural questions on extremal / critical (generalized) connections / metrics with respect to them. Explicit examples such as compact Lie groups ( [12], Hu [21]) could provide further insights into understanding these extensions. It should be worth exploring the interaction of the Riemannian, the complex and the Poisson geometric methods in generalized Hermitian geometry.…”