ABSTRACT
The purpose of this chapter is to study the main differential invariants of a surface in Euclidean space E3. This case contains the basic ingredients for the whole of modern differential geometry, and it is essentially distinct from the case of the curves since no simple canonical invariant parameterization is now available. However, we have seen in Sec. 2.3 that the invariants of a curve have a tensor interpretation, and therefore it will be natural to look for invariant tensors in the case of the surfaces as well.
