9626136 Corlette This proposal lies in the area of Kahler geometry. The geometry of a quotient space of the group of diffeomorphisms of the circle will be studied; minimal Lagrangian surfaces in complex projective and quaternionic spaces will be studied; the topology of geometrically finite quaternionic and Cayley hyperbolic manifolds will be also be investigated. Kahler geometry is the study of complex (sub-) manifolds equipped with a Kahler metric. A complex manifold is a curved space which looks locally like a complex number space; a Kahler metric then defines a distance function on the manifold compatible with its complex structure. It should be mentioned that many difficult calculations are possible only with the introduction of a complex strucure; a Kahler structure makes it possible to interpret these calculations geometrically. This is a very active area within the field of differential geometry with applications to parts of modern physics.
