Generalized Curvatures of Curves in $\mathbb{R}^n$
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914154352214016 |
|---|---|
| author | Teo, Lee-Peng |
| author_facet | Teo, Lee-Peng |
| contents | For a curve $\boldsymbolγ:I\to\mathbb{R}^n$ of order $n-1$, we prove that the generalized curvatures $κ_1, \ldots, κ_{n-1}$ can be expressed in terms of the leading principal minors of the matrix $\mathbf{A}(t)^T\mathbf{A}(t)$, where $\mathbf{A}(t)$ is the $n\times n$ matrix whose $i$-th column is $\boldsymbolγ^{(i)}(t)$. This gives an efficient algorithm to calculate the curvatures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09782 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Curvatures of Curves in $\mathbb{R}^n$ Teo, Lee-Peng Differential Geometry For a curve $\boldsymbolγ:I\to\mathbb{R}^n$ of order $n-1$, we prove that the generalized curvatures $κ_1, \ldots, κ_{n-1}$ can be expressed in terms of the leading principal minors of the matrix $\mathbf{A}(t)^T\mathbf{A}(t)$, where $\mathbf{A}(t)$ is the $n\times n$ matrix whose $i$-th column is $\boldsymbolγ^{(i)}(t)$. This gives an efficient algorithm to calculate the curvatures. |
| title | Generalized Curvatures of Curves in $\mathbb{R}^n$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2511.09782 |