\(B_n\)-generalized pseudo-Kähler structures (Q6113287)

The authors introduce the notions of \(B_n\)-generalized pseudo-Hermitian and \(B_n\)-generalized pseudo-Kählerian structure on an odd exact Courant algebroid, that is, a generalized tangent bundle. The Courant algebroids of type \(B_n\) represent the next simplest class of Courant algebroids, after generalized tangent bundles. They establish a criterion for a \(B_n\)-generalized almost pseudo-Hermitian structure to be \(B_n\)-generalized pseudo-Kähler, and obtain examples of \(B_n\)-generalized pseudo-Kähler structures on Courant algebroids of type \(B_n\) over Lie groups of dimension two, three and four. They also present some important results on left-invariant \(B_n\)-generalized pseudo-Kähler structures on Courant algebroids of type \(B_n\) over Lie groups of dimension two, three and four.