关于抛物曲面的微分不变式
On Differential Invariants of Parabolic Surfaces
摘要：
具有非零Pocchiola $4^{\text{th}}$不变量$W$的一般抛物曲面$S^2 \subset \mathbb{R}^3$的$SA_3(\mathbb{R})$下的微分不变式代数被证明是通过不变微分仅由另一个具有$57$微分单项式的$5$阶不变量$M$生成的。证明是基于Fels-Olver的递归公式，拉回到抛物射流束。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
