Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 307

Integrable deformations of affine surfaces via Nizhnik-Veselov-Novikov equation

B. G. Konopelchenko and U. Pinkall

It is shown that deformations ofaffine conormal according to the Nizhnik-Veselov-Novikov equation generate, via the Lelieuvrés formula, integrable deformations of affine surfaces. The total affine mean curvature is preserved by these deformations. It is shown that a stationary point of these deformations for centro-affine surfaces is given by the proper affine sphere.

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