George Sparling will continue his research in twistor theory. The twistor correspondence provides a means whereby complex analytic techniques may be brought to bear on questions of mathematical physics. This correspondence is achieved by thinking of the points of a Riemannian manifold as complex submanifolds of some associated complex manifold. Sparling will investigate whether or not the twistor complex manifolds associated with spacelike hypersurfaces in spacetime possess canonical Kaehler structures. He will also try to describe the twistor Cauchy Riemann structures directly in terms of pseudo-Riemannian geometry. Other related projects involve studies of the applications and ramifications of twistor theory to supergravity and string theory.
