Skip to main content
Log in

Flag curvatures on Berwald submersions

  • Published:
Periodica Mathematica Hungarica Aims and scope Submit manuscript

Abstract

In this paper, we give some fundamental equations of curvature tensors on Berwald submersions, which imply the relationship of flag curvatures of the associated manifolds and the fibers.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M. Abate, G. Patrizio, Finsler Metric—A Global Approach, vol. 1591, Lecture Notes in Math (Springer, Berlin, 1994)

    Book  Google Scholar 

  2. W. Ambrose, I.M. Singer, On homogeneous Riemannian manifolds. Duke Math. J. 25, 647–669 (1958)

    Article  MathSciNet  Google Scholar 

  3. W. Chen, X. Li, An Introduction to Riemann Ieometry (Peking University Press, Beijing, 2004). (in Chinese)

    Google Scholar 

  4. S.S. Chern, Z. Shen, Riemann–Finsler Geometry (World Scientific, Singapore, 2005)

    Book  Google Scholar 

  5. S. Deng, Z. Hou, Invariant Finsler metrics on homogeneous manifolds. J. Phys. A Math. Gen. 37, 8245–8253 (2004)

    Article  MathSciNet  Google Scholar 

  6. S. Deng, Z. Hou, On symmetric Finsler spaces. Isr. J. Math. 162, 197–219 (2007)

    Article  MathSciNet  Google Scholar 

  7. S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, 2nd edn. (Academic Press, London, 1978)

    MATH  Google Scholar 

  8. S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, vol. I (Interscience, New York, II, 1963)

    MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  10. Z. Szabó, Positive definite Berwald spaces (Structure Theorems on Berwald spaces). Tensor, N. S. 35, 25–39 (1981)

    MathSciNet  MATH  Google Scholar 

  11. R. Yan, Affinely equivalent K\(\ddot{a}\)hler-Finsler metrics on a complex manifold. Sci. China Math. 55, 731–738 (2012)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The author would like to thank the reviewer very much for his (her) helpful comments.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Rongmu Yan.

Additional information

Publisher's Note

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

Supported by the National Natural Science Foundation of China (11571287,11871405) and the Natural Science Foundation of Fujian Province of China (2016J01034).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yan, R. Flag curvatures on Berwald submersions. Period Math Hung 81, 115–122 (2020). https://doi.org/10.1007/s10998-020-00319-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10998-020-00319-0

Keywords

Mathematics Subject Classification

Navigation