Abstract
The aim of this paper is to characterize Kähler surfaces in terms oftheir positive twistor bundle. We prove that an oriented four-dimensionalRiemannian manifold (M, g) admits a complex structure J compatible with the orientation and such that (M, g, J is a Kähler manifold ifand only if the positive twistor bundle (Z +(M), g c ) admits a verticalKilling vector field.
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Jelonek, W. Positive Twistor Bundle of a Kähler Surface. Annals of Global Analysis and Geometry 22, 119–133 (2002). https://doi.org/10.1023/A:1019587610546
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DOI: https://doi.org/10.1023/A:1019587610546