Differential Invariants of Conformal and Projective Surfaces

Abstract

We show that, for both the conformal and projective groups, all the differential invariants of a generic surface in three-dimensional space can be written as combinations of the invariant derivatives of a single differential invariant. The proof is based on the equivariant method of moving frames.

Keywords

• conformal differential geometry
• projective differential geometry
• differential invariants
• moving frame
• syzygy
• differential algebra