manifolds and cobordisms
cobordism theory, Introduction
Definitions
Genera and invariants
Classification
Theorems
A generalization of the notion of Calabi-Yau manifold in the context of generalized complex geometry.
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
Spin(8)-subgroups and reductions to exceptional geometry
see also: coset space structure on n-spheres
The notion was introduced in
Relation to (non-integrable) G-structure for SU(n) (see also at MSU):
The role of generalized CY-manifolds as (factors of) target spaces in string theory is discussed for instance in
Mariana Graña, Ruben Minasian, Michela Petrini, Alessandro Tomasiello, Type II Strings and Generalized Calabi-Yau Manifolds (arXiv:hep-th/0409176)
Mariana Grana, Ruben Minasian, Michela Petrini, Alessandro Tomasiello, Generalized structures of N=1 vacua, hep-th/0505212
Jan Louis, Generalized Calabi-Yau compactifications with D-branes and fluxes, Forthschr. Phys. 53, no 7-8 (2005) (pdf)
Last revised on July 18, 2024 at 11:50:43. See the history of this page for a list of all contributions to it.