| Title:
|
How many are equiaffine connections with torsion (English) |
| Author:
|
Dušek, Zdeněk |
| Author:
|
Kowalski, Oldřich |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
51 |
| Issue:
|
5 |
| Year:
|
2015 |
| Pages:
|
265-271 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The question how many real analytic equiaffine connections with arbitrary torsion exist locally on a smooth manifold $M$ of dimension $n$ is studied. The families of general equiaffine connections and with skew-symmetric Ricci tensor, or with symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of $n$ variables. (English) |
| Keyword:
|
affine connection |
| Keyword:
|
Ricci tensor |
| Keyword:
|
Cauchy-Kowalevski Theorem |
| MSC:
|
35A10 |
| MSC:
|
35F35 |
| MSC:
|
35G50 |
| MSC:
|
35Q99 |
| idZBL:
|
Zbl 06537729 |
| idMR:
|
MR3449107 |
| DOI:
|
10.5817/AM2015-5-265 |
| . |
| Date available:
|
2016-01-11T10:02:21Z |
| Last updated:
|
2017-02-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144769 |
| . |
| Reference:
|
[1] Dušek, Z., Kowalski, O.: How many are torsion-less affine connections in general dimension.to appear in Adv. Geom. |
| Reference:
|
[2] Dušek, Z., Kowalski, O.: How many are affine connections with torsion.Arch. Math. (Brno) 50 (2014), 257–264. Zbl 1340.53021, MR 3303775, 10.5817/AM2014-5-257 |
| Reference:
|
[3] Egorov, Yu.V., Shubin, M.A.: Foundations of the Classical Theory of Partial Differential Equations.Springer-Verlag, Berlin, 1998. Zbl 0895.35003, MR 1657445 |
| Reference:
|
[4] Eisenhart, L.P.: Fields of parallel vectors in a Riemannian geometry.Trans. Amer. Math. Soc. 27 (4) (1925), 563–573. MR 1501329, 10.1090/S0002-9947-1925-1501329-4 |
| Reference:
|
[5] Helgason, S.: Differential Geometry, Lie Groups, and Symmetric Spaces.Amer. Math. Soc., 1978. Zbl 0451.53038, MR 1834454 |
| Reference:
|
[6] Kobayashi, S., Nomizu, N.: Foundations of differential geometry I., Wiley Classics Library, 1996. |
| Reference:
|
[7] Kowalevsky, S.: Zur Theorie der partiellen Differentialgleichung.J. Reine Angew. Math. 80 (1875), 1–32. |
| Reference:
|
[8] Kowalski, O., Sekizawa, M.: Diagonalization of three-dimensional pseudo-Riemannian metrics.J. Geom. Phys. 74 (2013), 251–255. Zbl 1280.53020, MR 3118584, 10.1016/j.geomphys.2013.08.010 |
| Reference:
|
[9] Mikeš, J., Vanžurová, A., Hinterleitner, I.: Geodesic Mappings and some Generalizations.Palacky University, Olomouc, 2009. Zbl 1222.53002, MR 2682926 |
| Reference:
|
[10] Nomizu, K., Sasaki, T.: Affine Differential Geometry.Cambridge University Press, 1994. Zbl 0834.53002, MR 1311248 |
| Reference:
|
[11] Petrovsky, I.G.: Lectures on Partial Differential Equations.Dover Publications, Inc., New York, 1991. MR 1160355 |
| . |
