Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 143

Discrete Isothermic Surfaces

A. Bobenko, U. Pinkall

J. reine angew. Math. 475 (1996) 187-208

Discrete isothermic surfaces are defined. It is shown that these discrete surfaces possess properties, which are characteristic for smooth isothermic surfaces (Moebius invariance, dual surface). Quaternionic zero-curvature loop group representations for smooth and discrete isothermic surfaces are presented. A Weierstrass type representation for discrete minimal isothermic surfaces is obtained and the discrete catenoid and the Enneper surface are constructed.

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