Bonnet theorem

This article is about the Bonnet theorem in the study of surfaces. For Bonnet's theorem in classical mechanics, see Bonnet's theorem. For Bonnet's diameter estimate, see Bonnet–Myers theorem. For Bonnet's theorem on the integral of curvature, see Gauss–Bonnet theorem.

In the mathematical field of differential geometry, the fundamental theorem of surface theory deals with the problem of prescribing the geometric data of a submanifold of Euclidean space. Originally proved by Pierre Ossian Bonnet in 1867, it has since been extended to higher dimensions and non-Euclidean contexts.