1. Twistor spaces of hyperka¨hler manifolds with <f>S1</f>-actions
- Author
-
Feix, Birte
- Subjects
- *
TWISTOR theory , *HOLOMORPHIC functions - Abstract
We shall describe the twistor space of a hyperka¨hler
4n -manifold with an isometricS1 -action which is holomorphic for one of the complex structures, scales the corresponding holomorphic symplectic form and whose fixed point set has complex dimensionn .We deduce that any hyperka¨hler metric on the cotangent bundle of a real-analytic Ka¨hler manifold which is compatible with the canonical holomorphic symplectic structure, extends the given Ka¨hler metric and for which theS1 -action by scalar multiplication in the fibres is isometric is unique in a neighbourhood of the zero section. These metrics have been constructed independently by the author and Kaledin. [Copyright &y& Elsevier]- Published
- 2003
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