| Title:
|
Metrization of connections with regular curvature (English) |
| Author:
|
Vanžurová, Alena |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
45 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
325-333 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We discuss Riemannian metrics compatible with a linear connection that has regular curvature. Combining (mostly algebraic) methods and results of [4] and [5] we give an algorithm which allows to decide effectively existence of positive definite metrics compatible with a real analytic connection with regular curvature tensor on an analytic connected and simply connected manifold, and to construct the family of compatible metrics (determined up to a scalar multiple) in the affirmative case. We also breafly touch related problems concerning geodesic mappings and projective structures. (English) |
| Keyword:
|
manifold |
| Keyword:
|
linear connection |
| Keyword:
|
metric |
| Keyword:
|
pseudo-Riemannian geometry |
| MSC:
|
53B05 |
| MSC:
|
53B20 |
| MSC:
|
53C05 |
| MSC:
|
53C20 |
| idZBL:
|
Zbl 1212.53020 |
| idMR:
|
MR2591685 |
| . |
| Date available:
|
2009-12-22T07:53:42Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137463 |
| . |
| Reference:
|
[1] Berger, M.: A Panoramic View of Riemannian Geometry.Springer, Berlin, Heidelberg, New York, 2003. Zbl 1038.53002, MR 2002701 |
| Reference:
|
[2] Borel, A., Lichnerowicz, A.: Groupes d’holonomie des variétés riemanniennes.C. R. Acad. Sci. Paris 234 (1952), 1835–1837. Zbl 0046.39801, MR 0048133 |
| Reference:
|
[3] Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry I, II.Wiley-Intersc. Publ., New York, Chichester, Brisbane, Toronto, Singapore, 1991. |
| Reference:
|
[4] Kowalski, O.: On regular curvature structures.Math. Z. 125 (1972), 129–138. Zbl 0234.53024, MR 0295250, 10.1007/BF01110924 |
| Reference:
|
[5] Kowalski, O.: Metrizability of affine connections on analytic manifolds.Note di Matematica 8 (1) (1988), 1–11. Zbl 0699.53038, MR 1050506 |
| Reference:
|
[6] Mikeš, J.: Geodesic mappings of affine-connected and Riemannian spaces.J. Math. Sci. 78 (1996), 311–333. MR 1384327, 10.1007/BF02365193 |
| Reference:
|
[7] Mikeš, J., Kiosak, V., Vanžurová, A.: Geodesic mappings of manifolds with affine connection.Palacký University, Olomouc (2008). Zbl 1176.53004, MR 2488821 |
| Reference:
|
[8] Schmidt, B. G.: Conditions on a connection to be a metric connection.Commun. Math. Phys. 29 (1973), 55–59. MR 0322726, 10.1007/BF01661152 |
| Reference:
|
[9] Vanžurová, A.: Metrization problem for linear connections and holonomy algebras.Arch. Math. (Brno) 44 (2008), 339–349. Zbl 1212.53021, MR 2501581 |
| Reference:
|
[10] Vilimová, Z.: The problem of metrizability of linear connections.Master's thesis, 2004, (supervisor: O. Krupková). |
| . |
