Type one generalized Calabi-Yaus

JOURNAL OF GEOMETRY AND PHYSICS

卷:120

Article

Bailey, Michael¹  Cavalcanti, Gil R.¹  Gualtieri, Marco² 

[1] Univ Utrecht, Utrecht, Netherlands

[2] Univ Toronto, Toronto, ON, Canada

关键词: Generalized complex structures;    Generalized Calabi-Yau;    Symplectic fibration;   

DOI  :  10.1016/j.geomphys.2017.03.012

来源: Elsevier

【 摘 要 】

We study type one generalized complex and generalized Calabi-Yau manifolds. We introduce a cohomology class that obstructs the existence of a globally defined, closed 2-form which agrees with the symplectic form on the leaves of the generalized complex structure, the twisting class. We prove that in a compact, type one, 4n-dimensional generalized complex manifold the Euler characteristic must be even and equal to the signature modulo four. The generalized Calabi-Yau condition places much stronger constraints: a compact type one generalized Calabi-Yau fibers over the 2-torus and if the structure has one compact leaf, then this fibration can be chosen to be the fibration by the symplectic leaves of the generalized complex structure. If the twisting class vanishes, one can always deform the structure so that it has a compact leaf. Finally we prove that every symplectic fibration over the 2-torus admits a type one generalized Calabi-Yau structure. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free