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2017 Twistor Spaces and Compact Manifolds Admitting Both Kähler and Non-Kähler Structures
Ljudmila Kamenova
J. Geom. Symmetry Phys. 46(none): 25-35 (2017). DOI: 10.7546/jgsp-46-2017-25-35

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.

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

Information

Published: 2017
First available in Project Euclid: 14 February 2018

MathSciNet: MR3791929
Digital Object Identifier: 10.7546/jgsp-46-2017-25-35

Rights: Copyright © 2017 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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