generalized Calabi-Yau manifold
Manifolds and cobordisms
A generalization of the notion of Calabi-Yau manifold in the context of generalized complex geometry.
In terms of -structure
For a -dimensional smooth manifold, a generalized complex structure on is a reduction of the structure group of the generalized tangent bundle along the inclusion
U(n,n) \hookrightarrow O(2n,2n)
into the Narain group.
Recall that for an ordinary compact complex manifold of real dimension , a Calabi-Yau manifold structure on is a reduction of the structure group along the inclusion of the special unitary group into the unitary group.
A generalized Calabi-Yau structure on a generalized complex manifold is a further reduction of the structure group along
SU(n,n) \hookrightarrow U(n,n) \hookrightarrow O(2n,2n)
(Hitchin, section 4.5)
The notion was introduced in
The role of generalized CY-manifolds as (factors of) target spaces in string theory is discussed for instance in
Revised on December 14, 2012 07:37:41
by Urs Schreiber