Claude LeBrun
Abstract
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A generalisation of the twistor construction of Einstein manifolds to the non-self-dual case is given. Specifically, it is shown that a complex Riemannian manifold is conformally Einstein if and only if there is a non-vanishing section of a certain rank-2 holomorphic vector bundle over its space of null geodesics.
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A generalisation of the twistor construction of Einstein manifolds to the non-self-dual case is given. Specifically, it is shown that a complex Riemannian manifold is conformally Einstein if and only if there is a non-vanishing section of a certain rank-2 holomorphic vector bundle over its space of null geodesics.
Key concepts: Physics, Twistor theory, Twistor space, Einstein, Mathematical physics, Holomorphic function, Rank (graph theory), Geodesic