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.
We define the notions of Bn-generalized pseudo-Hermitian and Bn-generalized pseudo-Kähler structure on an odd exact Courant algebroid E. When E is in the standard form (or of type Bn) 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 Bn-generalized pseudo-Kähler structures on Courant algebroids of type Bn over Lie groups of dimension two, three and four.