On Differential Invariants of Parabolic Surfaces

Zhangchi Chen (1) , Joël Merker (2)

1 LMO - Laboratoire de Mathématiques d'Orsay
2 DMA - Département de Mathématiques et Applications - ENS Paris

The algebra of differential invariants under $SA_3(\mathbb{R})$ 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.

Domaines: Mathématiques [math]; Géométrie différentielle [math.DG]

Zhangchi Chen, Joël Merker. On Differential Invariants of Parabolic Surfaces. 2020. ⟨hal-02455030⟩