Concrete Twistor Construction of Pseudo-Hyper-Kahler Metrics
A construction of a pseudo-hyper-Kahler structure directly on a given real manifold from a family of holomorphic symplectic forms parametrized by a complex variable, as a concrete variant of the Hitchin-Karlhede-Lindstrom-Rocek twistor theorem. Unlike the classical twistor theorem, which builds the manifold as a parameter space of twistor lines inside a twistor space, this approach works when the manifold is already in hand and shows the normal-bundle condition on holomorphic sections holds automatically.
2501.00505
This note proves a concrete variant of the Hitchin-Karlhede-Lindstrom-Rocek (HKLR) twistor theorem for constructing pseudo-hyper-Kahler metrics. In the classical theorem one starts from a twistor spa…