##### Department of Mathematics,

University of California San Diego

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### Differential Geometry Seminar

## Neil Donaldson

#### UC Irvine

## Isothermic submanifolds in Euclidean space

##### Abstract:

We give a positive answer to Burstall's question of whether there exists an interesting theory of isothermic submanifolds of dimension $>2$ in $R^n$. We relate chains of such manifolds to solutions of a system of PDEs and describe their moduli space. We also describe Christoffel and Darboux/Ribaucour transforms of isothermic chains.

### January 14, 2009

### 3:00 PM

### AP&M 5402

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