## Journal of Geometry and Symmetry in Physics

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

Ljudmila Kamenova

#### 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