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A curvature-ellipse-based Monge normal form of a regular surface in ℝ4 and its applications

  • Masaru Hasegawa
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Abstract

We study a Monge normal form of a surface in ℝ4 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 ℝ4 and to the geometry of their orthogonal projections.

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Cite

BibTeXRIS
BibTeX
@misc{hasegawa2026curvatureellipsebased,
  title = {{A curvature-ellipse-based Monge normal form of a regular surface in $\mathbbR^4$ and its applications}},
  author = {Masaru Hasegawa},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10132},
  eprint = {2610.10132},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10132},
}
RIS
TY  - UNPB
TI  - A curvature-ellipse-based Monge normal form of a regular surface in ℝ^4 and its applications
AU  - Masaru Hasegawa
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2610.10132
UR  - https://arxiv.org/abs/2610.10132
AB  - We study a Monge normal form of a surface in 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 ℝ^4 and to the geometry of their orthogonal projections.
ER  -