Journal of Geometry and Symmetry in Physics

Twistor Spaces and Compact Manifolds Admitting Both Kähler and Non-Kähler Structures

Ljudmila Kamenova

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Abstract

In this expository paper we review some twistor techniques and recall the problem of finding compact differentiable manifolds that can carry both Kähler and non-Kähler complex structures. Such examples were constructed independently by Atiyah, Blanchard and Calabi in the 1950’s. In the 1980’s Tsanov gave an example of a simply connected manifold that admits both Kähler and non-Kähler complex structures - the twistor space of a $K3$ surface. Here we show that the quaternion twistor space of a hyperkähler manifold has the same property.

Article information

Source
J. Geom. Symmetry Phys., Volume 46 (2017), 25-35.

Dates
First available in Project Euclid: 14 February 2018

Permanent link to this document
https://projecteuclid.org/euclid.jgsp/1518577291

Digital Object Identifier
doi:10.7546/jgsp-46-2017-25-35

Mathematical Reviews number (MathSciNet)
MR3791929

Citation

Kamenova, Ljudmila. Twistor Spaces and Compact Manifolds Admitting Both Kähler and Non-Kähler Structures. J. Geom. Symmetry Phys. 46 (2017), 25--35. doi:10.7546/jgsp-46-2017-25-35. https://projecteuclid.org/euclid.jgsp/1518577291


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