B_n-generalized pseudo-Kahler structures

TL;DR

This paper introduces B_n-generalized pseudo-Kahler structures on Courant algebroids, expressing them via classical tensors and exploring their invariant forms on low-dimensional Lie groups.

Contribution

It defines new B_n-generalized pseudo-Kahler structures and relates them to classical tensor fields, extending the bi-Hermitian perspective to this generalized setting.

Findings

Expressed structures in classical tensor terms

Described invariant structures on low-dimensional Lie groups

Extended bi-Hermitian viewpoint to B_n-generalized structures

Abstract

We define the notions of B_n-generalized pseudo-Hermitian and B_n-generalized pseudo-Kahler structures on an odd exact Courant algebroid E. When E is in the standard form (or of type B_n) we express these notions in terms of classical tensor fields on the base of E. This is analogous to the bi-Hermitian viewpoint on generalized Kahler structures on exact Courant algebroids. We describe left-invariant B_n-generalized pseudo-Kahler structures on Courant algebroids of type B_n over Lie groups of dimension two, three and four.