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On Cosymplectic-Like Statistical Submersions

  • Hülya Aytimur
  • Cihan ÖzgürEmail author
Article
  • 61 Downloads

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.

Keywords

Statistical manifold statistical submersion Kähler-like statistical manifold cosymplectic-like statistical manifold 

Mathematics Subject Classification

53B05 53B15 53C05 53A40 

Notes

References

  1. 1.
    Abe, N., Hasegawa, K.: An affine submersion with horizontal distribution and its applications. Differ. Geom. Appl. 14, 235–250 (2001)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Amari, S.: Differential-Geometrical Methods in Statistics. Springe, Berlin (1985)CrossRefGoogle Scholar
  3. 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. 4.
    Furuhata, H.: Hypersurfaces in statistical manifolds. Differ. Geom. Appl. 27(3), 420–429 (2009)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Gray, A.: Pseudo-Riemannian almost product manifolds and submersions. J. Math. Mech. 16, 715–737 (1967)MathSciNetzbMATHGoogle Scholar
  6. 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)MathSciNetCrossRefGoogle Scholar
  7. 7.
    O’Neill, B.: The fundamental equations of a submersion. Mich. Math. J. 13, 459–469 (1966)MathSciNetCrossRefGoogle Scholar
  8. 8.
    O’Neill, B.: Semi-Riemannian Geometry with Application to Relativity. Academic Press, New York (1983)zbMATHGoogle Scholar
  9. 9.
    Şahin, B.: Riemannian Submersions, Riemannian Maps in Hermitian Geometry and their Applications. Elsevier/Academic Press, London (2017)zbMATHGoogle Scholar
  10. 10.
    Takano, K.: Statistical manifolds with almost complex structures and its statistical submersions. Tensor (N.S.) 65, 123–137 (2004)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Takano, K.: Examples of the statistical submersion on the statistical model. Tensor (N.S.) 65(2), 170–178 (2004)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Takano, K.: Statistical manifolds with almost contact structures and its statistical submersions. J. Geom. 85(1–2), 171–187 (2006)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Vos, P.W.: Fundamental equations for statistical submanifolds with applications to the Bartlett correction. Ann. Inst. Stat. Math. 41(3), 429–450 (1989)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Yano, K., Kon, M.: Structures on Manifolds, Series in Pure Mathematics, vol. 3. World Scientific, Singapore (1984)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsBalıkesir UniversityBalıkesirTurkey

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