Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 298

Discrete Integrable Systems and Geometry

A. Bobenko

In XIIth International Congress of Mathematical Physics (ICMP ='97), eds. D. De Witt, A. Bracken, M. Gould, P. Pearce, International Press 1999, pp. 219-226

This is a summary of the talk given at the International Congress of Mathematical Physics '97, Brisbane, July 1997.In the first part it is shown how the loop group interpretationof the Baecklund transformations implies the existence of the correspondingdiscrete integrable geometries. In the second part discreteintegrable analogues of elastic curves and of the Lagrange top aredefined.

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