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Local Classification of Centroaffine Tchebychev Surfaces with Constant Curvature Metric

Binder, Thomas

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

We examine the centroaffine geometry of Tchebychev surfaces. By choosing local parameters adapted to the problem, it is possible to understand the integrability conditions. We introduce regular and singular surfaces and prove an existence theorem for regular ones. We will show that there are no Tchebychev surfaces with nonzero constant curvature metric, thus reducing the problem to $K=0$, which has already been solved.