Geodesic
Geometrical interpretations of a~torsion tensor, curvature tensors, and curvature pseudotensors in the generalized Finsler space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2013), pp. 31-40.

Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain geometrical interpretations for a torsion tensor and curvature tensors in the generalized Finsler space (with the non-symmetric main tensor).
Keywords: generalized Finsler space, non-symmetric connection, curvature tensor, curvature pseudotensor.
Mots-clés : torsion tensor 
@article{IVM_2013_1_a2,
     author = {S. M. Min\v{c}i\'c and M. L. Zlatanovi\'c},
     title = {Geometrical interpretations of a~torsion tensor, curvature tensors, and curvature pseudotensors in the generalized {Finsler} space},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {31--40},
     publisher = {mathdoc},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_1_a2/}
}
TY  - JOUR
AU  - S. M. Minčić
AU  - M. L. Zlatanović
TI  - Geometrical interpretations of a~torsion tensor, curvature tensors, and curvature pseudotensors in the generalized Finsler space
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2013
SP  - 31
EP  - 40
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2013_1_a2/
LA  - ru
ID  - IVM_2013_1_a2
ER  - 
%0 Journal Article
%A S. M. Minčić
%A M. L. Zlatanović
%T Geometrical interpretations of a~torsion tensor, curvature tensors, and curvature pseudotensors in the generalized Finsler space
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2013
%P 31-40
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2013_1_a2/
%G ru
%F IVM_2013_1_a2
S. M. Minčić; M. L. Zlatanović. Geometrical interpretations of a~torsion tensor, curvature tensors, and curvature pseudotensors in the generalized Finsler space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2013), pp. 31-40. http://geodesic.mathdoc.fr/item/IVM_2013_1_a2/

[1] Minčić S. M., Zlatanović M. Lj., “New commutation formulas for $\delta$-differentation in generalized Finsler space”, Differ. Geom. Dyn. Syst., 12 (2010), 145–157 | MR | Zbl

[2] Zlatanović M. Lj., Minčić S. M., “Identities for curvature tensors in generalized Finsler space”, Filomat, 23:2 (2009), 34–42 | DOI | MR | Zbl

[3] Rund Kh., Differentsialnaya geometriya Finslerovykh prostranstv, Nauka, M., 1981 | MR | Zbl

[4] Minčić S. M., Zlatanović M. Lj., “Derived curvature tensors in generalized Finsler space”, Differ. Geom. Dyn. Syst., 13 (2011), 179–190 | MR | Zbl

[5] Vacaru S. I., Einstein gravity, Lagrange–Finsler geometry, and nonsymmetric metrics on nonholonomic manifolds, 24 Jun. 2008, arXiv: 0806.3810v1[gr-qc] | MR

[6] Wanas M. I., “An AP-structure with Finslerian Flavor: I”, Modern Physics Letters A, 24:22 (2009), 1749–1762 | DOI | MR | Zbl

[7] Yoshihoro I., Il-Yong L., Hong-Suh P., “On generalized Finsler space structure with a vanishing $hv$-torsion”, J. Korean Math. Soc., 41:2 (2004), 369–378 | DOI | MR

[8] Youssef N. L., Sid-Ahmed Amr M., “Linear connections and curvature tensors in the geometry of parallelizable manifolds”, Reports Math. Physics, 60:1 (2007), 39–53 | DOI | MR | Zbl

[9] Zlatanović M. Lj., Minčić S. M., “Bianchi type identities in generalized Finsler space”, Hypercomplex numbers in geometry and physics, 7:2 (2010), 109–118 | MR

[10] Graif F., “Sulla posibilita di construire parallelogrami chiusi in alcune varieta a torsione”, Boll. Un. math. Ital. Ser. III, 7 (1952), 132–135 | MR | Zbl

[11] Cartan E., Les Espaces de Finsler, Paris, 1934

[12] Einstein A., “Bianchi identities in the generalized theory of gravitation”, Canad. J. Math., 2:2 (1950), 120–128 | DOI | MR | Zbl

[13] Einstein A., “Relativistic theory of the non-symmetric field”, Appendix II in the book, The meaning of relativity, 5th Ed., Princeton, 1955, 49

[14] Einstein A., “Generalization of the relativistic theory of gravitation”, Ann. math. (2) (Princeton), 46:4 (1945), 576–584 | MR

[15] Eisenhart L. P., “Generalized Riemann spaces”, Proc. Nat. Acad. Sci. USA, 37:5 (1951), 311–315 | DOI | MR | Zbl

[16] Minchich S. M., “Geometricheskie interpretatsii tenzorov i psevdotenzorov krivizny prostranstva nesimmetrichnoi affinnoi svyaznosti”, Publ. Inst. Math. (Beograd), 47(61) (1990), 113–120 | MR

[17] Prvanovich M., “Chetyre tenzora krivizny nesimmetricheskoi svyaznosti”, 150 let geometrii Lobachevskogo, Sb. (Kazan, 1976), Moskva, 1977, 199–205