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note on Bn-geometry
Actually, the developments show that there need not be a new name at all, as this is just part of T-duality, as is kown now. But since people still refer to it as “$B_n$-geometry”, there needs to be an entry that says what is meant by this name.
Of course you can’t help that it’s called that, but I agree it’s not a great name. My first association would be an incidence geometry modeled on a Coxeter group in the $B_n$ series. I guess it’s not that.
Actually it is. Plain generalized complex geometry is controled by the structure group of the generalized tangent bundle of a manifold, which is $SO(n,n)$ and hence of type $D_n$. Here now one adds a line bundle to this (the Poincare line bundle of the T-duality correspondence) and so the structure group becomes $SO(n+1,n)$, of type $B_n$.
I have added a brief note to this extent to the entry.
Oh, thanks! So it is a good name after all.
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