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arXiv · 1711.07948

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 M. Atiyah, A. Blanchard and E. Calabi in the $1950$'s. In the $1980$'s V. 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. 2017-12-19. Twistor spaces and compact manifolds admitting both Kähler and non-Kähler structures. https://arxiv.org/abs/1711.07948

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