| Title:
|
Tangent Lie algebras to the holonomy group of a Finsler manifold (English) |
| Author:
|
Muzsnay, Zoltán |
| Author:
|
Nagy, Péter T. |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
19 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
137-147 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Our goal in this paper is to make an attempt to find the largest Lie algebra of vector fields on the indicatrix such that all its elements are tangent to the holonomy group of a Finsler manifold. First, we introduce the notion of the curvature algebra, generated by curvature vector fields, then we define the infinitesimal holonomy algebra by the smallest Lie algebra of vector fields on an indicatrix, containing the curvature vector fields and their horizontal covariant derivatives with respect to the Berwald connection. At the end we introduce conjugates of infinitesimal holonomy algebras by parallel translations with respect to the Berwald connection. We prove that this holonomy algebra is tangent to the holonomy group. (English) |
| Keyword:
|
higher order field theories |
| Keyword:
|
boundary terms |
| MSC:
|
22E65 |
| MSC:
|
53B40 |
| MSC:
|
53C29 |
| idZBL:
|
Zbl 1247.53026 |
| idMR:
|
MR2897266 |
| . |
| Date available:
|
2012-04-06T06:18:49Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142097 |
| . |
| Reference:
|
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| Reference:
|
[2] Crampin, M., Saunders, D.J.: Holonomy of a class of bundles with fibre metrics. arXiv: 1005.5478v1 |
| Reference:
|
[3] Kozma, L.: Holonomy structures in Finsler geometry, Part 5. Handbook of Finsler Geometry , P.L. Antonelli (ed.)445-490 Kluwer Academic Publishers, Dordrecht 2003 MR 2066448 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[6] Muzsnay, Z., Nagy, P.T.: Finsler manifolds with non-Riemannian holonomy. Houston J. Math |
| Reference:
|
[7] Shen, Z.: Differential Geometry of Spray and Finsler Spaces. Kluwer Academic Publishers, Dordrecht 2001 Zbl 1009.53004, MR 1967666 |
| Reference:
|
[8] Szabó, Z.I.: Positive definite Berwald spaces. Tensor , New Ser., 35 1981 25-39 Zbl 0464.53025, MR 0614132 |
| . |
