$$B_{n}$$-Generalized Pseudo-Kähler Structures

Abstract

AbstractWe define the notions of $$B_{n}$$ B n -generalized pseudo-Hermitian and $$B_{n}$$ B n -generalized pseudo-Kähler structure on an odd exact Courant algebroid E. When E is in the standard form (or of type $$B_{n}$$ 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 Kähler structures on exact Courant algebroids. We describe left-invariant $$B_{n}$$ B n -generalized pseudo-Kähler structures on Courant algebroids of type $$B_{n}$$ B n over Lie groups of dimension two, three and four.