On Differential Invariants of Parabolic Surfaces

Zhangchi Chen; Joël Merker

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arXiv · 1908.07867

On Differential Invariants of Parabolic Surfaces

Zhangchi Chen·Joël Merker

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Abstract

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.

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Zhangchi Chen, Joël Merker. 2019-08-21. On Differential Invariants of Parabolic Surfaces. https://arxiv.org/abs/1908.07867

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