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
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
(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