| Title:
|
Geodesic mapping onto Kählerian spaces of the first kind (English) |
| Author:
|
Zlatanović, Milan |
| Author:
|
Hinterleitner, Irena |
| Author:
|
Najdanović, Marija |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
4 |
| Year:
|
2014 |
| Pages:
|
1113-1122 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present paper a generalized Kählerian space $\mathbb {G} {\underset 1 {\mathbb {K}}_N}$ of the first kind is considered as a generalized Riemannian space $\mathbb {GR}_N$ with almost complex structure $\smash {F^h_i}$ that is covariantly constant with respect to the first kind of covariant derivative. \endgraf Using a non-symmetric metric tensor we find necessary and sufficient conditions for geodesic mappings $f\colon \mathbb {GR}_N\to \mathbb {G}\underset 1{\mathbb {\overline {K}}}_N$ with respect to the four kinds of covariant derivatives. These conditions have the form of a closed system of partial differential equations in covariant derivatives with respect to unknown components of the metric tensor and the complex structure of the Kählerian space $\mathbb {G}{\underset 1 {\mathbb {K}}}_N$. (English) |
| Keyword:
|
geodesic mapping |
| Keyword:
|
equitorsion geodesic mapping |
| Keyword:
|
generalized Kählerian space |
| MSC:
|
53B05 |
| MSC:
|
53B35 |
| idZBL:
|
Zbl 06433717 |
| idMR:
|
MR3304801 |
| DOI:
|
10.1007/s10587-014-0156-z |
| . |
| Date available:
|
2015-02-09T17:45:37Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144164 |
| . |
| Reference:
|
[1] Domašev, V. V., Mikeš, J.: On the theory of holomorphically projective mappings of Kählerian spaces.Math. Notes 23 (1978), 160-163 translated from Matematicheskie Zametki 23 (1978), Russian 297-303. MR 0492674, 10.1007/BF01153160 |
| Reference:
|
[2] Einstein, A.: The Meaning of Relativity.Princeton University Press Princeton, N. J. (1955). Zbl 0067.20404, MR 0076496 |
| Reference:
|
[3] Einstein, A.: The Bianchi identities in the generalized theory of gravitation.Can. J. Math. 2 (1950), 120-128. Zbl 0039.38802, MR 0034134, 10.4153/CJM-1950-011-4 |
| Reference:
|
[4] Einstein, A.: A generalization of the relativistic theory of gravitation.Ann. Math. (2) 46 (1945), 578-584. Zbl 0060.44113, MR 0014296, 10.2307/1969197 |
| Reference:
|
[5] Eisenhart, L. P.: Generalized Riemann spaces.Proc. Natl. Acad. Sci. USA 37 (1951), 311-315. Zbl 0043.37301, MR 0043530, 10.1073/pnas.37.5.311 |
| Reference:
|
[6] Hinterleitner, I., Mikeš, J.: On {$F$}-planar mappings of spaces with affine connections.Note Mat. 27 (2007), 111-118. Zbl 1150.53009, MR 2367758 |
| Reference:
|
[7] Mikeš, J.: Holomorphically projective mappings and their generalizations.J. Math. Sci., New York 89 (1998), 1334-1353 translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory 30 (1995), Russian. MR 1619720, 10.1007/BF02414875 |
| Reference:
|
[8] Mikeš, J.: Geodesic mappings of affine-connected and Riemannian spaces.J. Math. Sci., New York 78 (1996), 311-333 translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory 11 (1994), Russian. MR 1384327, 10.1007/BF02365193 |
| Reference:
|
[9] Mikeš, J.: Geodesic mappings of Ricci 2-symmetric Riemannian spaces.Math. Notes 28 (1981), 922-924 translated from Matematicheskie Zametki 28 313-317 (1980), Russian. MR 0587405 |
| Reference:
|
[10] Mikeš, J., Starko, G. A.: $K$-concircular vector fields and holomorphically projective mappings on Kählerian spaces.Proceedings of the 16th Winter School on ``Geometry and Physics'', Srn'ı, Czech Republic, 1996 Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 46 Palermo (1997), 123-127 Jan Slovák et al. MR 1469028 |
| Reference:
|
[11] Mikeš, J., Vanžurová, A., Hinterleitner, I.: Geodesic Mappings and Some Generalizations.Palacký University, Faculty of Science Olomouc (2009). Zbl 1222.53002, MR 2682926 |
| Reference:
|
[12] Minčić, S. M.: New commutation formulas in the non-symmetric affine connexion space.Publ. Inst. Math., Nouv. Sér. 22 (1977), 189-199. Zbl 0377.53008, MR 0482552 |
| Reference:
|
[13] Minčić, S. M.: Ricci identities in the space of non-symmetric affine connexion.Mat. Vesn., N. Ser. 10 (1973), 161-172. Zbl 0278.53012, MR 0341310 |
| Reference:
|
[14] Minčić, S. M., Stanković, M. S.: Equitorsion geodesic mappings of generalized Riemannian spaces.Publ. Inst. Math., Nouv. Sér. 61 (1997), 97-104. Zbl 0886.53035, MR 1472941 |
| Reference:
|
[15] Minčić, S., Stanković, M.: On geodesic mappings of general affine connexion spaces and of generalized Riemannian spaces.Mat. Vesn. 49 (1997), 27-33. Zbl 0949.53013, MR 1491944 |
| Reference:
|
[16] Minčić, S. M., Stanković, M. S., Velimirović, L. S.: Generalized Kählerian spaces.Filomat 15 (2001), 167-174. MR 2105108 |
| Reference:
|
[17] Moffat, J. W.: Gravitational theory, galaxy rotation curves and cosmology without dark matter.J. Cosmol. Astropart. Phys. (electronic only) 2005 (2005), Article No. 003, 28 pages. Zbl 1236.83045, MR 2139872 |
| Reference:
|
[18] Ōtsuki, T., Tashiro, Y.: On curves in Kaehlerian spaces.Math. J. Okayama Univ. 4 (1954), 57-78. Zbl 0057.14101, MR 0066024 |
| Reference:
|
[19] Prvanović, M.: A note on holomorphically projective transformations of the Kähler spaces.Tensor, New Ser. 35 (1981), 99-104. Zbl 0467.53032, MR 0614141 |
| Reference:
|
[20] Pujar, S. S.: On non-metric semi-symmetric complex connection in a Kaehlerian manifold.Bull. Calcutta Math. Soc. 91 (1999), 313-322. Zbl 0957.53039, MR 1748542 |
| Reference:
|
[21] Pušić, N.: On a curvature-type invariant of a family of metric holomorphically semi-symmetric connections on anti-Kähler spaces.Indian J. Math. 54 (2012), 57-74. Zbl 1268.53020, MR 2976295 |
| Reference:
|
[22] Sinjukov, N. S.: Geodesic mappings of Riemannian spaces.Nauka Moskva Russian (1979). MR 0552022 |
| Reference:
|
[23] Stanković, M. S., Minčić, S. M., Velimirović, L. S.: On equitorsion holomorphically projective mappings of generalised Kählerian spaces.Czech. Math. J. 54 (2004), 701-715. MR 2086727, 10.1007/s10587-004-6419-3 |
| Reference:
|
[24] Stanković, M. S., Zlatanović, M. L., Velimirović, L. S.: Equitorsion holomorphically projective mappings of generalized Kählerian space of the first kind.Czech. Math. J. 60 (2010), 635-653. Zbl 1224.53031, MR 2672406, 10.1007/s10587-010-0059-6 |
| Reference:
|
[25] Tashiro, Y.: On a holomorphically projective correspondence in an almost complex space.Math. J. Okayama Univ. 6 (1957), 147-152. Zbl 0077.35501, MR 0087181 |
| Reference:
|
[26] Yano, K.: Differential Geometry on Complex and Almost Complex Spaces.International Series of Monographs in Pure and Applied Mathematics 49 Pergamon Press, Macmillan, New York (1965). Zbl 0127.12405, MR 0187181 |
| . |
