Mathematical Sciences: Harmonic Maps, Kahler Manifolds and Hermitian Locally Symmetric Spaces

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The principal investigator will study harmonic maps on a compact Riemannian manifold which is either Kahler or Riemannian locally symmetric. He will attempt to obtain new Bochner identities to prove geometric rigidity theorems in optimal for quotients of Riemannian symmetric manifolds of rank greater than one. His methods are different than standard methods in the line of research since he does not require that the manifolds under consideration be folliated by bounded symmetric domains. This award will support research in the general area of differential geometry and global analysis. Differential geometry is the study of the relationship between the geometry of a space and analytic concepts defined on the space. Global analysis is the study of the overall geometric and topological properties of a space by piecing together local information. Applications of these areas of mathematics in other sciences include the structure of complicated molecules, liquid-gas boundaries, and the large scale structure of the universe.