Mathematical Sciences: On Certain Rigidity Problems in Kaehler Geometry

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The uniformization theorem of one complex variable completely classifies the one dimensional simply connected complex manifolds. There is no corresponding result for higher dimensional complex manifolds and it is important to try to find some method which will provide a substitute classification. The principal investigator will try to classify those higher dimensional complex manifolds which satisfy a pinched curvature condition. Classification of a set of objects which satisfy a common property or condition is one tool mathematicians use to understand structures and their relationships. If one can list all objects which have a restricted common property, then one better understands the property and the objects. The principal investigator will attempt to do this with manifolds or surfaces whose curvature falls between certain bounds.