## The Momentum Construction for Circle-Invariant Kähler Metrics |

**Andrew D. Hwang, College of the Holy Cross**

November 14, 2002

4:30 pm

Bailey Hall 102

Refreshments in the common room at 4:00 pm

It is rare in differential geometry to have a concrete description of a metric; homogeneous spaces are perhaps the best-known examples. This talk introduces an explicit construction of Kähler metrics that are "almost" homogeneous in the sense that their geometry is essentially specified by solving an ordinary differential equation. The key idea is to write the (unknown) metric in terms of its own "momentum" function, τ. In these coordinates, the scalar curvature is second-orderlinearin the defining data of the metric. Consequently, it is relatively easy to construct complete metrics of specified (e.g., constant) scalar curvature.Much of the talk is joint work with Michael A. Singer.

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