| Title:
|
Special Einstein’s equations on Kähler manifolds (English) |
| Author:
|
Hinterleitner, Irena |
| Author:
|
Kiosak, Volodymyr |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
46 |
| Issue:
|
5 |
| Year:
|
2010 |
| Pages:
|
333-337 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This work is devoted to the study of Einstein equations with a special shape of the energy-momentum tensor. Our results continue Stepanov’s classification of Riemannian manifolds according to special properties of the energy-momentum tensor to Kähler manifolds. We show that in this case the number of classes reduces. (English) |
| Keyword:
|
Einstein’s equations |
| Keyword:
|
Kähler manifolds |
| Keyword:
|
pseudo-Riemannian spaces |
| Keyword:
|
Riemannian spaces |
| MSC:
|
32Q15 |
| MSC:
|
35Q76 |
| MSC:
|
53B20 |
| MSC:
|
53B30 |
| MSC:
|
53B35 |
| MSC:
|
53B50 |
| idZBL:
|
Zbl 1249.53015 |
| idMR:
|
MR2753987 |
| . |
| Date available:
|
2010-12-14T15:04:30Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141387 |
| . |
| Reference:
|
[1] Eisenhart, L. P.: Non-Riemannian Geometry.Princeton University Press, 1926, Amer. Math. Soc. Colloquium Publications 8 (2000). MR 1466961 |
| Reference:
|
[2] Hall, G. S.: Lorentz manifolds and general relativity theory.Differential geometry (Warsaw, 1979), Banach Center Publ. 12 (1984), 47–52. Zbl 0546.53050, MR 0961072 |
| Reference:
|
[3] Mikeš, J.: Holomorphically projective mappings and their generalizations.J. Math. Sci. 89 (3) (1998), 1334–1353. MR 1619720, 10.1007/BF02414875 |
| Reference:
|
[4] Mikeš, J., Vanžurová, A., Hinterleitner, I.: Geodesic mappings and some generalizations.Palacky University Press, Olomouc, 2009. Zbl 1222.53002, MR 2682926 |
| Reference:
|
[5] Petrov, A. Z.: New methods in the general theory of relativity.Nauka, Moscow, 1966. MR 0207365 |
| Reference:
|
[6] Reboucas, M. J., Santos, J., Teixeira, A. F. F.: Classification of energy momentum tensors in $n\ge 5$ dimensional space-time: a review.Brazil. J. Phys. 34 (2A) (2004), 535–543. 10.1590/S0103-97332004000300034 |
| Reference:
|
[7] Schouten, J. A., Struik, D. J.: Einführung in die neueren Methoden der Differentialgeometrie.Groningen, P. Noordhoff, 1935. Zbl 0011.17404 |
| Reference:
|
[8] Stepanov, S. E.: The seven classes of almost symplectic structures.Webs and quasigroups, Tver. Gos. Univ., Tver', 1992, pp. 93–96. Zbl 0862.53030, MR 1227168 |
| Reference:
|
[9] Stepanov, S. E.: On a group approach to studying the Einstein and Maxwell equations.Theoret. and Math. Phys. 111 (1) (1997), 419–427. MR 1473424, 10.1007/BF02634197 |
| Reference:
|
[10] Stepanov, S. E., Tsyganok, I. I.: The seven classes of the Einstein equations.arXiv:1001.4673v1. |
| Reference:
|
[11] Yano, K.: Differential geometry of complex and almost comlex spaces.Pergamon Press, 1965. |
| . |
