On Differential Invariants of Parabolic Surfaces

Zhangchi Chen; Joël Merker

On Differential Invariants of Parabolic Surfaces

Differential Geometry 2020-07-31 v3

Authors: Zhangchi Chen , Joël Merker

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.

Cite

@article{arxiv.1908.07867,
  title  = {On Differential Invariants of Parabolic Surfaces},
  author = {Zhangchi Chen and Joël Merker},
  journal= {arXiv preprint arXiv:1908.07867},
  year   = {2020}
}

Comments

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

On Differential Invariants of Parabolic Surfaces

Abstract

Cite

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