| Title:
|
Automorphisms of Spacetime Manifold with Torsion (English) |
| Author:
|
Pan’Zhenskii, Vladimir Ivanovich |
| Author:
|
Surina, Olga Petrovna |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
87-94 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we prove that the maximum dimension of the Lie group of automorphisms of the Riemann–Cartan 4-dimensional manifold does not exceed 8, and if the Cartan connection is skew-symmetric or semisymmetric, the maximum dimension is equal to 7. In addition, in the case of the Riemann–Cartan $n$-dimensional manifolds with semisymmetric connection the maximum dimension of the Lie group of automorphisms is equal to $n(n-1)/2+1$ for any $n>2$. (English) |
| Keyword:
|
Riemann–Cartan manifolds |
| Keyword:
|
automorphisms |
| Keyword:
|
semi-symmetric connection |
| MSC:
|
53C05 |
| MSC:
|
53C25 |
| idZBL:
|
Zbl 1365.53023 |
| idMR:
|
MR3674603 |
| . |
| Date available:
|
2016-08-30T11:58:30Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145820 |
| . |
| Reference:
|
[1] Gordeeva, I. A., Pan’zhenskii, V. I., Stepanov, S. E.: Riemann–Cartan manifolds.. In: Modern Mathematics and Its Applications 123 Geometry, VINITI, Moscow, 2009, 110–141, (in Russian). MR 2866744 |
| Reference:
|
[2] Tamm, I. E.: On the curved momentum space.. In: Selected Papers 4, Springer-Verlag, Berlin, Heidelberg, 1991, 197–210; Selected Scientific Papers 2, Nauka, Moscow, 1975, 218–225. |
| Reference:
|
[3] Tamm, I. E., Vologodskii, V. G.: On the use of curved momentum space in the construction of nonlocal Euclidean field theory.. In: Collection of Scientific Papers 2, Nauka, Moscow, 1975, 226–253, (in Russian). Princeton Univ. Press, Princetton, NJ, 1953; Inostrannaya Literatura, Moscow, 1957. |
| Reference:
|
[4] Pan’zhenskii, V. I.: Maximally movable Riemannian spaces with torsion.. Math. Notes 85, 5-6 (2010), 720–723; Mat. Zametki 85, 5 (2009), 754–757. MR 2572865 |
| Reference:
|
[5] Pan’zhenskii, V. I.: Automorphisms of the Riemann–Cartan space-time manifold.. Tr. Mezhdunar. Geom. Tsentra 5, 2 (2012), 27–34. |
| Reference:
|
[6] Pan’zhenskii, V. I.: Automorphisms of Riemann-Cartan Manifolds with Semi-Symmetric Connection.. Journal of Mathematical Physics, Analysis, Geometry 10, 2 (2014), 233–239. MR 3236968 |
| Reference:
|
[7] Pan’zhenskii, V. I.: Automorphisms of Riemann–Cartan Manifolds.. Math. Notes 98, 4 (2015), 613–623. Zbl 1337.53045, MR 3438511, 10.1134/S000143461509028X |
| Reference:
|
[8] Yano, K., Bochner, S.: Curvature and Betti Numbers.. Princeton Univ. Press, Princetton, NJ, 1953; Inostrannaya Literatura, Moscow, 1957. Zbl 0051.39402, MR 0062505 |
| Reference:
|
[9] Stepanov, S. E., Gordeeva, I. A.: Pseudo-Killing and pseudoharmonic vector Fields on a Riemann–Cartan manifold.. Math. Notes 87, 1-2 (2010), 248–257; Mat. Zametki 87, 2 (2010), 267–279. Zbl 1197.53049, MR 2731477, 10.1134/S0001434610010311 |
| . |
