Integrable Complex Structures on Twistor Spaces

2012/12/17 by Gindi, Steven
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1212.4138

Abstract

We introduce integrable complex structures on twistor spaces fibered over complex manifolds. We then show, in particular, that the twistor spaces associated with generalized Kahler, SKT and strong HKT manifolds all naturally admit complex structures. Moreover, in the strong HKT case we construct a metric and three compatible complex structures on the twistor space that have equal torsions.

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• Compatible Complex Structures on Twistor Spaces
• Espaces de twisteurs des structures complexes généralisées
• Product twistor spaces and Weyl geometry
• Twistor Spaces of Riemannian Manifolds with Even Clifford Structures
• Generalized metrics and generalized twistor spaces