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"Nice Metrics on Kahler Manifolds or Why I Still Love Calculus''

by

Christina Tonnesen-Friedman
Union College

February 5, 2007
4:45pm
Bailey Hall 201

Refreshments will be served in Bailey 204


Abstract:

In (higher dimensional) spaces that are only locally like R^n (so-called manifolds) we cannot do Euclidean geometry. However for smooth manifolds there is always some kind of geometry present ... in fact many different ones! To remedy this ambiguity, one puts additional requirements on the geometry - usually related to curvature and inspired by physics. In the best of cases this allows us to define a canonical geometry on the manifold. Given a manifold and given the requirements, it is, however, often a daunting task (if not impossible) to find the geometry that fits, or at least to find out if it exists and if it is unique. This talk will cover some examples of manifolds where the additional requirements (namely Weakly Bochner Flatness or, more generally, Extremality) happen to be manageable and yield "just really annoying calculus exercises''. The talk will be accessible to anyone with a basic calculus background.


For additional information, send e-mail to math@union.edu or call (518) 388-6246.
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