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Title: Equitorsion holomorphically projective mappings of generalized Kählerian space of the first kind (English)
Author: Stanković, Mića S.
Author: Zlatanović, Milan Lj.
Author: Velimirović, Ljubica S.
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 60
Issue: 3
Year: 2010
Pages: 635-653
Summary lang: English
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Category: math
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Summary: In this paper we define generalized Kählerian spaces of the first kind $(G\underset 1K_N)$ given by (2.1)--(2.3). For them we consider hollomorphically projective mappings with invariant complex structure. Also, we consider equitorsion geodesic mapping between these two spaces ($G\underset 1K_N$ and $G\underset 1{\overline K}_N$) and for them we find invariant geometric objects. (English)
Keyword: generalized Riemannian space
Keyword: Kählerian space
Keyword: generalized Kählerian space of the first kind
Keyword: equitorsion holomorphically projective mappings
Keyword: holomorphically projective parameter.
MSC: 53B05
MSC: 53B35
idZBL: Zbl 1224.53031
idMR: MR2672406
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Date available: 2010-07-20T17:05:43Z
Last updated: 2020-07-03
Stable URL: http://hdl.handle.net/10338.dmlcz/140595
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Reference: [1] Chodorová, M., Mikeš, J.: A note to K-torse forming vector fields on compact manifolds with complex structure.Acta Physica Debrecina 42 (2008), 11-18. MR 2754424
Reference: [2] 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: [3] Einstein, A.: Die Grundlage der allgemeinen Relativitätstheorie.Ann. Phys. 49 (1916), 769-822. 10.1002/andp.19163540702
Reference: [4] Einstein, A.: Relativistic theory of the non-symmetic field.In: The Meaning of Relativity, 5th ed., Appendix II, Vol. 49 Princeton University Press Princeton (1955).
Reference: [5] Einstein, A.: Generalization of the relativistic theory of gravitation.Ann. Math. 46 (1945), 578-584. Zbl 0060.44113, MR 0014296, 10.2307/1969197
Reference: [6] Eisenhart, L. P.: Generalized Riemannian spaces.Proc. Natl. Acad. Sci. 37 (1951), 311-315. MR 0043530, 10.1073/pnas.37.5.311
Reference: [7] Hinterleitner, I., Mikeš, J.: On $F$-planar mappings of spaces with affine connections.Note Mat. 27 (2007), 111-118. MR 2367758
Reference: [8] Hinterleitner, I., Mikeš, J., Stránská, J.: Infinitesimal $F$-planar transformations.Russ. Math. 52 (2008), 13-18. MR 2445169, 10.3103/S1066369X08040026
Reference: [9] Jukl, M., Juklová, L., Mikeš, J.: On Generalized Trace Decompositions Problems. Proc. 3rd International Conference dedicated to 85th birthday of Professor Kudrijavcev.(2008), 299-314.
Reference: [10] Mikeš, J.: Holomorphically projective mappings and their generalizations.J. Math. Sci. 89 (1998), 1334-1353. MR 1619720, 10.1007/BF02414875
Reference: [11] Mikeš, J., Starko, G. A.: $K$-concircular vector fields and holomorphically projective mappings on Kählerian spaces.Suppl. Rend. Circ. Palermo 46 (1997), 123-127. MR 1469028
Reference: [12] Minči'c, S. M.: Ricci identities in the space of non-symmetric affine connection.Mat. Ves. 10 (1973), 161-172. MR 0341310
Reference: [13] Minči'c, S. M.: New commutation formulas in the non-symmetric affine connection space.Publ. Inst. Math. (N. S) 22 (1977), 189-199. MR 0482552
Reference: [14] Minči'c, S. M.: Independent curvature tensors and pseudotensors of spaces with non-symmetric affine connection.Coll. Math. Soc. János Bolyai 31 (1982), 445-460. MR 0706937
Reference: [15] Minčić, S. M., Stanković, M. S., Velimirović, Lj. S.: Generalized Kählerian spaces.Filomat 15 (2001), 167-174. MR 2105108
Reference: [16] Otsuki, T., Tasiro, Y.: On curves in Kählerian spaces.Math. J. Okayama Univ. 4 (1954), 57-78. MR 0066024
Reference: [17] Prvanovi'c, M.: A note on holomorphically projective transformations in Kähler space.Tensor, N.S. 35 (1981), 99-104. MR 0614141
Reference: [18] Radulovi'c, Zh.: Holomorphically-projective mappings of parabolically-Kählerian spaces.Math. Montisnigri 8 (1997), 159-184. MR 1623833
Reference: [19] Shiha, M.: On the theory of holomorphically projective mappings of parabolically Kählerian spaces.In: Differential Geometry and Its Applications. Proc. 5th International Conference, Opava, August 24-28, 1992 Silesian University Opava (1993), 157-160. Zbl 0805.53017, MR 1255537
Reference: [20] Sinyukov, N. S.: Geodesic Mappings of Riemannian Spaces.Nauka Moscow (1979), Russian. Zbl 0637.53020, MR 0552022
Reference: [21] Stanković, M. S., Minčić, S. M., Velimirović, Lj. S.: On equitorsion holomorphically projective mappings of generalized Kählerian spaces.Czech. Math. J. 54(129) (2004), 701-715. MR 2086727, 10.1007/s10587-004-6419-3
Reference: [22] Vavříková, H., Mikeš, J., Pokorná, O., Starko, G.: On fundamental equations of almost geodesic mappings of type $\pi_2(e)$.Russ. Math. 51 (2007), 8-12. MR 2335593, 10.3103/S1066369X07010021
Reference: [23] Yano, K.: Differential Geometry of Complex and Almost Complex Spaces.Pergamon Press New York (1965). MR 0187181
Reference: [24] Yano, K.: On complex conformal connections.Kodai Math. Semin. Rep. 26 (1975), 137-151. Zbl 0302.53013, MR 0377736, 10.2996/kmj/1138846996
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