Skip to main content
SpringerLink
Log in

New Form of the Basic Equations of Almost Geodesic Mappings of the Second Type

  • Published:
Mediterranean Journal of Mathematics Aims and scope Submit manuscript

Abstract

In the present paper, almost geodesic mappings of the second type of spaces with non-symmetric affine connection are considered. A new form of the basic equations of these mappings was found using the Nijenhuis tensor. Also, Nijenhuis tensors of the first and second kind were introduced.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Berezovski, V.E., Mikeš, J.: On the classification of almost geodesic mapings of affine connection spaces. Acta Univ. Palacki. Olomouc. Fac. Rer. Nat. Math. 35(1), 21–24 (1996)

    MATH  Google Scholar 

  2. Berezovski, V.E., Mikeš, J.: On special almost geodesic mappings of type \(\pi _1\) of spaces with affine connection. Acta Univ. Palacki. Olomouc. Fac. Rer. Nat. Math. 43(1), 21–26 (2004)

    Google Scholar 

  3. Berezovski, V.E., Mikeš, J.: Almost geodesic mappings of spaces with affine connection. J. Math. Sci. 207(3), 389–409 (2015)

    Article  MathSciNet  Google Scholar 

  4. Berezovski, V.E., Mikeš, J., Vanžurová, A.: Fundamental PDE’s of the canonical almost geodesic mappings of type \({\tilde{\pi }}_1\). Bull. Malays. Math. Sci. Soc. (2) 37(3), 647–659 (2014)

    MathSciNet  MATH  Google Scholar 

  5. Einstein, A.: Relativistic Theory of the Non-symmetric Field, Append. II in The Meaning of Relativity, 5th edn. Princeton University Press, Princeton (1955)

    Google Scholar 

  6. Eisenhart, L.P.: Non-Riemannian geometry. American Mathematical Society, New York (1927)

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

    Article  Google Scholar 

  8. Hinterleitner, I., Mikeš, J.: Geodesic mappings and Einstein Spaces. Geometric Methods in Physics, Trends in Mathematics, pp. 331–335 (2013)

    Google Scholar 

  9. Mikeš, J.: Geodesic mappings of affine-connected and Riemannian spaces. J. Math. Sci. N. Y. 78(3), 311–333 (1996)

    Article  MathSciNet  Google Scholar 

  10. Mikeš, J.: Holomorphically projective mappings and their generalizations. J. Math. Sci. N. Y. 89(3), 1334–1353 (1998)

    Article  MathSciNet  Google Scholar 

  11. Mikeš, J., Pokorná, O., Starko, G.: On almost geodesic mappings \(\pi _2(e)\) onto Riemannian spaces. Rendiconti del circolo matematico di Palermo Serie II(Suppl. 72), 151–157 (2004)

    MATH  Google Scholar 

  12. Mikeš, J., Vanžurová, A., Hinterleitner, I.: Geodesic Mappings and Some Generalizations. University Printing, Olomouc (2009)

    MATH  Google Scholar 

  13. Mikeš, J., et al.: Differential Geometry of Special Mappings. Palacký University Press, Olomouc (2015)

    MATH  Google Scholar 

  14. Minčić, S.M.: Independent curvature tensors and pseudotensors of spaces with non-symmetric affine connexion. Colloquia Mathematica Societatis János Bolayai, 31, Differential Geometry, Budapest (Hungary), pp. 445–460 (1979)

  15. Minčić, S.M.: Ricci identities in the space of non-symmetric affine connexion. Mat. Vesn. 10(25), 161–172 (1973)

    MathSciNet  MATH  Google Scholar 

  16. Minčić, S.M.: Some characteristics of curvature tensors of non-symmetric affine connexion. 12th Yugoslav Geometrical Seminar (Novi Sad, 1998). Novi Sad J. Math. 6(3), 169–183 (1999)

    Google Scholar 

  17. Minčić, S.M.: On Ricci type identities in manifolds with non-symmetric affine connection. Publ. Inst. Math. (Beograd) (N.S.) 94(108), 205–217 (2013)

    Article  MathSciNet  Google Scholar 

  18. Minčić, S.M., Stanković, M.S., Velimirović, LjS: Generalized Kahlerian spaces. Filomat 15, 167–174 (2001)

    MATH  Google Scholar 

  19. Minčić, S.M., Stanković, M.S., Velimirović, Lj.S.: Generalized Riemannian spaces and spaces of non-symmetric affine connection, University of Niš, Faculty of Science and Mathenatics, Niš (2013)

  20. Petrović, M.Z., Stanković, M.S.: Special almost geodesic mappings of the first type of non-symmetric affine connection spaces. Bull. Malays. Math. Sci. Soc. (2) 40(3), 1353–1362 (2017)

    Article  MathSciNet  Google Scholar 

  21. Prvanović, M.: Four curvature tensors of non-symmetric affine connexion. In: Proc. Conf. “150 years of Lobachevski geometry”, pp. 199–205. Kazan 1976, Moscow (1977) (in Russian)

  22. Sinyukov, N.S.: Geodesic mappings of Riemannian spaces. Nauka, Moscow (1979). (in Russian)

    MATH  Google Scholar 

  23. Sobchuk, V.S., Mikeš, J., Pokorná, O.: On almost geodesic mappings \(\pi _2\) between semisymmetric Riemannian spaces. Novi Sad J. Math. 29(3), 309–312 (1999)

    MathSciNet  MATH  Google Scholar 

  24. Stanković, M.S.: Almost geodesic mappings of the first type of affine spaces. Novi Sad J. Math. 29(3), 313–323 (1999)

    MathSciNet  MATH  Google Scholar 

  25. Stanković, M.S.: On a canonic almost geodesic mappings of the second type of affine spaces. Filomat 13, 105–114 (1999)

    MathSciNet  MATH  Google Scholar 

  26. Stanković, M.S.: On a special almost geodesic mappings of the third type of affine spaces. Novi Sad J. Math. 31(2), 125–135 (2001)

    MathSciNet  MATH  Google Scholar 

  27. Stanković, M.S.: Special equitorsion almost geodesic mappings of the third type of non-symmetric affine connection spaces. Appl. Math. Comput. 244, 695–701 (2014)

    MathSciNet  MATH  Google Scholar 

  28. Stanković, M.S., Minčić, S.M., Velimirović, LjS: On holomorphically projective mappings of generalized Kählerian spaces. Mat. Vesn. 54, 195–202 (2002)

    MATH  Google Scholar 

  29. Stanković, M.S., Minčić, S.M., Velimirović, L.S.: On equitorsion holomorphically projective mappings of generalized Kählerian spaces. Czechoslov. Math. J. 54(129), 701–715 (2004)

    Article  Google Scholar 

  30. Stanković, M.S., Vesić, N.O.: Some relations in non-symmetric affine connection spaces with regard to a special almost geodesic mappings of the third type. Filomat 29(9), 1941–1951 (2015)

    Article  MathSciNet  Google Scholar 

  31. Vavříková, H., Mikeš, J., Pokorná, O., Starko, G.: On fundamental equations of almost geodesic mappings of type \(\pi {}_2(e)\). Russ. Math. 51(1), 8–12 (2007). (Transl. from Iz. VUZ Matematika, No. 1, (2007), 10–15)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, Niš, 18000, Serbia

    Vladislava M. Stanković

Authors
  1. Vladislava M. Stanković
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vladislava M. Stanković.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Stanković, V.M. New Form of the Basic Equations of Almost Geodesic Mappings of the Second Type. Mediterr. J. Math. 17, 23 (2020). https://doi.org/10.1007/s00009-019-1453-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00009-019-1453-4

Keywords

Mathematics Subject Classification

Search

Navigation