Differential Invariants of Conformal and Projective Surfaces

TL;DR

This paper demonstrates that all differential invariants of generic surfaces under conformal and projective groups can be generated from a single invariant using invariant derivatives, utilizing the equivariant moving frames method.

Contribution

It establishes a unifying framework showing that a single differential invariant suffices to generate all invariants for conformal and projective surface actions.

Findings

All invariants derive from a single invariant and its derivatives.

The proof employs the equivariant moving frames method.

Results apply to generic surfaces in three-dimensional space.

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.