3. Bonnet Surfaces in Euclidean Three-space

Abstract

The Bonnet theorem characterizes surfaces via the coefficients e ^u,H,Q of their fundamental forms. These coefficients are not independent and are subject to the Gauss-Codazzi equations. A natural question is whether some of these data are superfluous. For example, do the metric e ^u and the mean curvature function H alone suffice to describe a surface completely? This problem was posed first by Bonnet who was able to find a partial solution to it.