Mathematical Sciences: Homogeneous Complex Manifolds and Isoparametric Hypersurfaces in Spheres and Nonlinear PartialDifferential Equations

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Josef Dorfmeister will carry out research in three areas. These concern homogeneous complex manifolds, isoparametric hypersurfaces in spheres and nonlinear partial differential equations. Dorfmeister, in collaboration with Nakajima and Neher has recently achieved remarkable results concerning homogeneous Kahler manifolds and certain isoparametric triple systems. He will continue to apply algebraic and functional analytic techniques to related problems. In particular he will try to determine all Kahler structures on manifolds which admit a transitive group of automorphisms. The second major project will be to describe all Lie algebras which occur as infinitesimal automorphisms of some homogeneous Kahler manifold. The final part of the program concerns an investigation of the class of contractible, rational, homogeneous domains in complex n-dimensional space.