Skip to main content
SpringerLink
Log in

On Cosymplectic-Like Statistical Submersions

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

Abstract

We study cosymplectic-like statistical submersions. It is shown that for a cosymplectic-like statistical submersion, the base space is a Kähler-like statistical manifold and each fiber is a cosymplectic-like statistical manifold. We find the characterizations of the total and the base spaces under certain conditions. Examples of cosymplectic-like statistical manifolds and their submersions are also given.

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. Abe, N., Hasegawa, K.: An affine submersion with horizontal distribution and its applications. Differ. Geom. Appl. 14, 235–250 (2001)

    Article  MathSciNet  Google Scholar 

  2. Amari, S.: Differential-Geometrical Methods in Statistics. Springe, Berlin (1985)

    Book  Google Scholar 

  3. Besse, A.L.: Einstein Manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 10. Springer, Berlin (1987)

    Google Scholar 

  4. Furuhata, H.: Hypersurfaces in statistical manifolds. Differ. Geom. Appl. 27(3), 420–429 (2009)

    Article  MathSciNet  Google Scholar 

  5. Gray, A.: Pseudo-Riemannian almost product manifolds and submersions. J. Math. Mech. 16, 715–737 (1967)

    MathSciNet  MATH  Google Scholar 

  6. Murathan, C., Şahin, B.: A study of Wintgen like inequality for submanifolds in statistical warped product manifolds. J. Geom. 109(2), Art. 30 (2018)

    Article  MathSciNet  Google Scholar 

  7. O’Neill, B.: The fundamental equations of a submersion. Mich. Math. J. 13, 459–469 (1966)

    Article  MathSciNet  Google Scholar 

  8. O’Neill, B.: Semi-Riemannian Geometry with Application to Relativity. Academic Press, New York (1983)

    MATH  Google Scholar 

  9. Şahin, B.: Riemannian Submersions, Riemannian Maps in Hermitian Geometry and their Applications. Elsevier/Academic Press, London (2017)

    MATH  Google Scholar 

  10. Takano, K.: Statistical manifolds with almost complex structures and its statistical submersions. Tensor (N.S.) 65, 123–137 (2004)

    MathSciNet  MATH  Google Scholar 

  11. Takano, K.: Examples of the statistical submersion on the statistical model. Tensor (N.S.) 65(2), 170–178 (2004)

    MathSciNet  MATH  Google Scholar 

  12. Takano, K.: Statistical manifolds with almost contact structures and its statistical submersions. J. Geom. 85(1–2), 171–187 (2006)

    Article  MathSciNet  Google Scholar 

  13. Vos, P.W.: Fundamental equations for statistical submanifolds with applications to the Bartlett correction. Ann. Inst. Stat. Math. 41(3), 429–450 (1989)

    Article  MathSciNet  Google Scholar 

  14. Yano, K., Kon, M.: Structures on Manifolds, Series in Pure Mathematics, vol. 3. World Scientific, Singapore (1984)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Balıkesir University, 10145, Balıkesir, Turkey

    Hülya Aytimur & Cihan Özgür

Authors
  1. Hülya Aytimur
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cihan Özgür
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cihan Özgür.

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

Aytimur, H., Özgür, C. On Cosymplectic-Like Statistical Submersions. Mediterr. J. Math. 16, 70 (2019). https://doi.org/10.1007/s00009-019-1332-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00009-019-1332-z

Keywords

Mathematics Subject Classification

Search

Navigation