| Title:
|
General-affine invariants of plane curves and space curves (English) |
| Author:
|
Kobayashi, Shimpei |
| Author:
|
Sasaki, Takeshi |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
67-104 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present a fundamental theory of curves in the affine plane and the affine space, equipped with the general-affine groups ${\rm GA}(2)={\rm GL}(2,{\mathbb R})\ltimes {\mathbb R}^2$ and ${\rm GA}(3)={\rm GL}(3,{\mathbb R})\ltimes {\mathbb R}^3$, respectively. We define general-affine length parameter and curvatures and show how such invariants determine the curve up to general-affine motions. We then study the extremal problem of the general-affine length functional and derive a variational formula. We give several examples of curves and also discuss some relations with equiaffine treatment and projective treatment of curves. (English) |
| Keyword:
|
plane curve |
| Keyword:
|
space curve |
| Keyword:
|
general-affine group |
| Keyword:
|
general-affine curvature |
| Keyword:
|
variational problem |
| MSC:
|
53A15 |
| MSC:
|
53A20 |
| MSC:
|
53A55 |
| idZBL:
|
07217122 |
| idMR:
|
MR4078347 |
| DOI:
|
10.21136/CMJ.2019.0165-18 |
| . |
| Date available:
|
2020-03-10T10:14:50Z |
| Last updated:
|
2022-04-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148043 |
| . |
| Reference:
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