Higher dimensional generalizations of twistor spaces

Hai Lin Tsinghua University Tao Zheng Universite Grenoble Alpes, France

Mathematical Physics mathscidoc:1702.22015

J.Geom.Phys., 114, 492-505, 2017.4
We construct a generalization of twistor spaces of hypercomplex manifolds and hyper-Kahler manifolds M, by generalizing the twistor P1 to a more general complex manifold Q. The resulting manifold X is complex if and only if Q admits a holomorphic map to P1. We make branched double covers of these manifolds. Some class of these branched double covers can give rise to non-Kahler Calabi-Yau manifolds. We show that these manifolds X and their branched double covers are non-Kahler. In the cases that Q is a balanced manifold, the resulting manifold X and its special branched double cover have balanced Hermitian metrics.
twistor spaces, string models, Hermitian metrics, holomorphic maps, hypercomplex manifolds, hyper-Kahler manifolds
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  • http://www.sciencedirect.com/science/article/pii/S0393044016303394
  title={Higher dimensional generalizations of twistor spaces},
  author={Hai Lin, and Tao Zheng},
Hai Lin, and Tao Zheng. Higher dimensional generalizations of twistor spaces. 2017. Vol. 114. In J.Geom.Phys.. pp.492-505. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170225221632326782516.
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