On Twistor Spaces of Anti-Self-Dual Hermitian Surfaces
Open Access
- 1 June 1992
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 331 (2) , 653-661
- https://doi.org/10.2307/2154133
Abstract
We consider a complex surface with anti-self-dual hermitian metric and study the holomorphic properties of its twistor space . We show that the naturally defined divisor line bundle is isomorphic to the power of the canonical bundle of , if and only if there is a Kähler metric of zero scalar curvature in the conformal class of . This has strong consequences on the geometry of , which were also found by C. Boyer using completely different methods. We also prove the existence of a very close relation between holomorphic vector fields on and in the case that is compact and Kähler.Keywords
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