| Title:
|
Metrizability of connections on two-manifolds (English) |
| Author:
|
Vanžurová, Alena |
| Author:
|
Žáčková, Petra |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
48 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
157-170 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We contribute to the reverse of the Fundamental Theorem of Riemannian geometry: if a symmetric linear connection on a manifold is given, find non-degenerate metrics compatible with the connection (locally or globally) if there are any. The problem is not easy in general. For nowhere flat $2$-manifolds, we formulate necessary and sufficient metrizability conditions. In the favourable case, we describe all compatible metrics in terms of the Ricci tensor. We propose an application in the calculus of variations. (English) |
| Keyword:
|
Manifold |
| Keyword:
|
linear connection |
| Keyword:
|
metric connection |
| Keyword:
|
pseudo-Riemannian geometry |
| MSC:
|
53B05 |
| MSC:
|
53B20 |
| MSC:
|
53C05 |
| idZBL:
|
Zbl 1195.53023 |
| idMR:
|
MR2641956 |
| . |
| Date available:
|
2010-02-11T14:00:46Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137517 |
| . |
| Reference:
|
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| . |
