发表机构
Iwate Medical University（岩手医科大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于曲率椭圆主轴的 $\mathbb{R}^4$ 中曲面 Monge 标准形，仅用欧氏运动和局部重参数化保持曲率椭圆不变量，并应用于 $2$-jet 几何与正交投影几何。
AI 中文摘要
我们研究了基于曲率椭圆主轴构造的 $\mathbb{R}^4$ 中曲面的 Monge 标准形。该标准形仅利用环境空间的欧氏运动和曲面的局部重新参数化获得，并保持曲率椭圆的欧氏不变量，包括其半轴长度（直至其顺序）。我们还给出了该标准形在 $\mathbb{R}^4$ 中曲面的 $2$-jet 几何及其正交投影几何中的应用。
英文摘要
We study a Monge normal form of a surface in $\mathbb{R}^4$ based on the principal axes of its curvature ellipse. The curvature-ellipse-based Monge normal form is obtained using only Euclidean motions of the ambient space and local reparameterizations of the surface, and preserves the Euclidean invariants of the curvature ellipse, including its semi-axis lengths up to their ordering. We also give applications of this normal form to the $2$-jet geometry of surfaces in $\mathbb{R}^4$ and to the geometry of their orthogonal projections.
