| Title:
|
Shells of monotone curves (English) |
| Author:
|
Mikeš, Josef |
| Author:
|
Strambach, Karl |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
3 |
| Year:
|
2015 |
| Pages:
|
677-699 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We determine in $\mathbb {R}^n$ the form of curves $C$ corresponding to strictly monotone functions as well as the components of affine connections $\nabla $ for which any image of $C$ under a compact-free group $\Omega $ of affinities containing the translation group is a geodesic with respect to $\nabla $. Special attention is paid to the case that $\Omega $ contains many dilatations or that $C$ is a curve in $\mathbb {R}^3$. If $C$ is a curve in $\mathbb {R}^3$ and $\Omega $ is the translation group then we calculate not only the components of the curvature and the Weyl tensor but we also decide when $\nabla $ yields a flat or metrizable space and compute the corresponding metric tensor. (English) |
| Keyword:
|
geodesic |
| Keyword:
|
shell of a curve |
| Keyword:
|
affine connection |
| Keyword:
|
(pseudo-)Riemannian metric |
| Keyword:
|
projective equivalence |
| MSC:
|
51H20 |
| MSC:
|
53B05 |
| MSC:
|
53B20 |
| MSC:
|
53B30 |
| MSC:
|
53C22 |
| idZBL:
|
Zbl 06537686 |
| idMR:
|
MR3407599 |
| DOI:
|
10.1007/s10587-015-0202-5 |
| . |
| Date available:
|
2015-10-04T18:09:08Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144437 |
| . |
| Reference:
|
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| . |
