On the recovery of a surface with prescribed first and second fundamental forms. (Q1408915)

The paper proves Bonnet's theorem as a corollary of the known theorem which states that if the Riemann-Christoffel tensor associated with a field of positive definite symmetric matrices of order three vanishes in a connected and simply connected open set in \(\mathbb{R}^3\), then this field is the metric tensor field of an open set that can be isometrically imbedded in \(\mathbb{R}^3\) uniquely up to rigid motions.