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Equitorsion holomorphically projective mappings of generalized Kählerian space of the first kind

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Abstract

In this paper we define generalized Kählerian spaces of the first kind (\( G_1^K N \)) 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 (\( G_1^K N \) and \( G_1^{\bar K} N \)) and for them we find invariant geometric objects.

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References

  1. M. Chodorová, J. Mikeš: A note to K-torse forming vector fields on compact manifolds with complex structure. Acta Physica Debrecina 42 (2008), 11–18.

    Google Scholar 

  2. A. Einstein: The Bianchi identities in the generalized theory of gravitation. Can. J. Math. 2 (1950), 120–128.

    MATH  MathSciNet  Google Scholar 

  3. A. Einstein: Die Grundlage der allgemeinen Relativitätstheorie. Ann. Phys. 49 (1916), 769–822.

    Article  Google Scholar 

  4. A. Einstein: Relativistic theory of the non-symmetic field. In: The Meaning of Relativity, 5th ed., Appendix II, Vol. 49. Princeton University Press, Princeton, 1955.

    Google Scholar 

  5. A. Einstein: Generalization of the relativistic theory of gravitation. Ann. Math. 46 (1945), 578–584.

    Article  MathSciNet  Google Scholar 

  6. L.P. Eisenhart: Generalized Riemannian spaces. Proc. Natl. Acad. Sci. 37 (1951), 311–315.

    Article  MATH  MathSciNet  Google Scholar 

  7. I. Hinterleitner, J. Mikeš: On F-planar mappings of spaces with affine connections. Note Mat. 27 (2007), 111–118.

    MATH  MathSciNet  Google Scholar 

  8. I. Hinterleitner, J. Mikeš, J. Stránská: Infinitesimal F-planar transformations. Russ. Math. 52 (2008), 13–18.

    Article  MATH  Google Scholar 

  9. M. Jukl, L. Juklová, J. Mikeš: On Generalized Trace Decompositions Problems. Proc. 3rd International Conference dedicated to 85th birthday of Professor Kudrijavcev. 2008, pp. 299–314.

  10. J. Mikeš: Holomorphically projective mappings and their generalizations. J. Math. Sci. 89 (1998), 1334–1353.

    Article  MATH  Google Scholar 

  11. J. Mikeš, G.A. Starko: K-concircular vector fields and holomorphically projective mappings on Kählerian spaces. Suppl. Rend. Circ. Palermo 46 (1997), 123–127.

    Article  Google Scholar 

  12. S.M. Minčić: Ricci identities in the space of non-symmetric affine connection. Mat. Ves. 10 (1973), 161–172.

    Google Scholar 

  13. S.M. Minčić: New commutation formulas in the non-symmetric affine connection space. Publ. Inst. Math. (N. S) 22 (1977), 189–199.

    Google Scholar 

  14. S.M. Minčić: Independent curvature tensors and pseudotensors of spaces with non-symmetric affine connection. Coll. Math. Soc. János Bolyai 31 (1982), 445–460.

    Google Scholar 

  15. S.M. Minčić, M. S. Stanković, Lj. S. Velimirović: Generalized Kählerian spaces. Filomat 15 (2001), 167–174.

    MATH  Google Scholar 

  16. T. Otsuki, Y. Tasiro: On curves in Kählerian spaces. Math. J. Okayama Univ. 4 (1954), 57–78.

    MATH  MathSciNet  Google Scholar 

  17. M. Prvanović: A note on holomorphically projective transformations in Kähler space. Tensor, N.S. 35 (1981), 99–104.

    MATH  MathSciNet  Google Scholar 

  18. Zh. Radulović: Holomorphically-projective mappings of parabolically-Kählerian spaces. Math. Montisnigri 8 (1997), 159–184.

    MATH  MathSciNet  Google Scholar 

  19. M. Shiha: 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, pp. 157–160.

    Google Scholar 

  20. N. S. Sinyukov: Geodesic Mappings of Riemannian Spaces. Nauka, Moscow, 1979. (In Russian.)

    MATH  Google Scholar 

  21. M. S. Stanković, S.M. Mincić, Lj. S. Velimirović: On equitorsion holomorphically projective mappings of generalized Kählerian spaces. Czech. Math. J. 54(129) (2004), 701–715.

    Article  MATH  Google Scholar 

  22. H. VavřÍková, J. Mikeš, O. Pokorná, G. Starko: On fundamental equations of almost geodesic mappings of type π2(e). Russ. Math. 51 (2007), 8–12.

    Article  Google Scholar 

  23. K. Yano: Differential Geometry of Complex and Almost Complex Spaces. Pergamon Press, New York, 1965.

    Google Scholar 

  24. K. Yano: On complex conformal connections. Kodai Math. Semin. Rep. 26 (1975), 137–151.

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Faculty of Science and Mathematics, Višegradska 33, 18000, Niš, Serbia

    Mića S. Stanković, Milan Lj. Zlatanović & Ljubica S. Velimirović

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  1. Mića S. Stanković
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  2. Milan Lj. Zlatanović
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  3. Ljubica S. Velimirović
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Correspondence to Mića S. Stanković.

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Authors were supported by Project 144032 MNTR Serbia.

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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, 635–653 (2010). https://doi.org/10.1007/s10587-010-0059-6

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  • DOI: https://doi.org/10.1007/s10587-010-0059-6

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