On Differential Invariants of Parabolic Surfaces

Abstract

The algebra of differential invariants under $S{A}_3(\mathbb{R})$ of generic parabolic surfaces $S^2\subset {\mathbb{R}}^3$ with nonvanishing Pocchiola $4^{\text{th}}$ invariant $W$ is shown to be generated, through invariant differentiations, by only one other invariant, $M$, of order $5$, having $57$ differential monomials. The proof is based on Fels-Olver's recurrence formulas, pulled back to the parabolic jet bundles.

This work was supported in part by the Polish National Science Centre (NCN) via the grant number 2018/29/B/ST1/02583. 104 Pages, >10 figures, explicit expressions and algorithms