November 7, 2002
This talk will be a warm-up to Prof. Hwang's talk next week. I will try to give a rough introduction to Kähler geometry and to discuss some of the questions people are interested in in this field.
Kähler geometry may be viewed as a link between Riemannian geometry, complex (algebraic) geometry and symplectic topology; a Kähler structure on a given manifold provides us with a Riemannian metric, a complex structure, and a symplectic 2-form.
A key question to ask is the following: On a complex manifold admitting Kähler structures, which Kähler structure is "nicest"?
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