Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
Einstein’s equations; Kähler manifolds; pseudo-Riemannian spaces; Riemannian spaces
Einstein’s equations; Kähler manifolds; pseudo-Riemannian spaces; Riemannian spaces
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.
References:
[1] Eisenhart, L. P.: Non-Riemannian Geometry. Princeton University Press, 1926, Amer. Math. Soc. Colloquium Publications 8 (2000). MR 1466961
[2] Hall, G. S.: Lorentz manifolds and general relativity theory. Differential geometry (Warsaw, 1979), Banach Center Publ. 12 (1984), 47–52. MR 0961072 | Zbl 0546.53050
[3] Mikeš, J.: Holomorphically projective mappings and their generalizations. J. Math. Sci. 89 (3) (1998), 1334–1353. DOI 10.1007/BF02414875 | MR 1619720
[4] Mikeš, J., Vanžurová, A., Hinterleitner, I.: Geodesic mappings and some generalizations. Palacky University Press, Olomouc, 2009. MR 2682926 | Zbl 1222.53002
[5] Petrov, A. Z.: New methods in the general theory of relativity. Nauka, Moscow, 1966. MR 0207365
[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. DOI 10.1590/S0103-97332004000300034
[7] Schouten, J. A., Struik, D. J.: Einführung in die neueren Methoden der Differentialgeometrie. Groningen, P. Noordhoff, 1935. Zbl 0011.17404
[8] Stepanov, S. E.: The seven classes of almost symplectic structures. Webs and quasigroups, Tver. Gos. Univ., Tver', 1992, pp. 93–96. MR 1227168 | Zbl 0862.53030
[9] Stepanov, S. E.: On a group approach to studying the Einstein and Maxwell equations. Theoret. and Math. Phys. 111 (1) (1997), 419–427. DOI 10.1007/BF02634197 | MR 1473424
[10] Stepanov, S. E., Tsyganok, I. I.: The seven classes of the Einstein equations. arXiv:1001.4673v1.
[11] Yano, K.: Differential geometry of complex and almost comlex spaces. Pergamon Press, 1965.
Search
Partner of
