| Title:
|
Homogeneous Geodesics in 3-dimensional Homogeneous Affine Manifolds (English) |
| Author:
|
Dušek, Zdeněk |
| Author:
|
Kowalski, Oldřich |
| Author:
|
Vlášek, Zdeněk |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
29-42 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For studying homogeneous geodesics in Riemannian and pseudo-Riemannian geometry (on reductive homogeneous spaces) there is a simple algebraic formula which works, at least potentially, in every given case. In the affine differential geometry, there is not such a universal formula. In the previous work, we proposed a simple method of investigation of homogeneous geodesics in homogeneous affine manifolds in dimension 2. In the present paper, we use this method on certain classes of homogeneous connections on the examples of 3-dimensional Lie groups. (English) |
| Keyword:
|
affine connection |
| Keyword:
|
affine Killing vector field |
| Keyword:
|
homogeneous manifold |
| Keyword:
|
homogeneous geodesic |
| MSC:
|
53B05 |
| MSC:
|
53C30 |
| idZBL:
|
Zbl 1244.53057 |
| idMR:
|
MR2920697 |
| . |
| Date available:
|
2011-12-08T09:46:19Z |
| Last updated:
|
2013-09-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141718 |
| . |
| Reference:
|
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| Reference:
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