Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 263

Discrete Affine Spheres

A. I. Bobenko, W. K. Schief

In: A.I. Bobenko, R. Seiler (eds.) Discrete Integrable Geometry and Physics, Oxford University Press 1999, pp. 113-138

Integrable discrete versions of affine spheres are constructed. It is shown that the underlying discrete Gauss-Codazzi equations reduce to an integrable discrete Tzitzeica system. A Backlund transformation generating discrete affine spheres is obtained in a purely algebraic manner and an interpretation of the Gauss equations for discrete affine spheres in terms of loop groups is recorded.

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