A curvature-ellipse-based Monge normal form of a regular surface in $\mathbb{R}^4$ and its applications
Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Hasegawa, Masaru
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220921719