The principal investigator will study the algebraic structure of twistor spaces, the construction of Kahler Einstein metrics and application of Kahler reduction. The methods to be employed are a combination of differential geometry and algebraic techniques. A twistor space is a complex three dimensional space associated to a self-dual Riemannian four dimensional manifold. The principal investigator will study those twistor spaces associated with the connected sums of complex projective planes. The principal investigator will also study the construction of Kahler Einstein metrics on spaces admitting a one parameter group of symmetries. The general theory of relativity is set in spaces in which curvature is proportional to stress. These spaces, called Einstein manifolds, arise in many branches of mathematics and it is useful to know when a given space has the structure of an Einstein space. The principal investigator will study this question as well as the structure of other spaces which arise in mathematical physics.
