Skip to main content
Log in

Hypersurface of a Finsler Space Subjected to a Kropina Change with an h-Vector

  • Research Article
  • Published:
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Aims and scope Submit manuscript

Abstract

The concept of h-vector was introduced by Izumi (Tensor NS 34:337–359, 1980). Recently we have obtained the Cartan connection for the Finsler space whose metric is given by Kropina change with an h-vector. Matsumoto (J Math Kyoto Univ 25–1:107–144, 1985) studied the theory of Finsler hypersurface. In this paper, we derive certain geometrical properties of a Finslerian hypersurface subjected to a Kropina change with an h-vector.

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

Notes

  1. Numbers in square brackets refer to the references at the end of the paper.

References

  1. Shibata C (1984) On invariant tensors of \(\beta \)-changes of Finsler metrics. J Math Kyoto Univ 24–1:163–188

    Article  MathSciNet  MATH  Google Scholar 

  2. Kropina VK (1961) On projective two-dimensional Finsler spaces with special metric. Trudy Sem Vector Tensor Anal 11:277–292 (in Russian)

    MathSciNet  Google Scholar 

  3. Izumi H (1980) Conformal transformations of Finsler spaces II. An h-conformally flat Finsler space. Tensor NS 34:337–359

    MathSciNet  MATH  Google Scholar 

  4. Gupta MK, Pandey PN (2015) Finsler space subjected to a Kropina change with an h-vector. Facta Univ (NIŠ) Ser Math Inform 30(4):513–525

    MathSciNet  MATH  Google Scholar 

  5. Matsumoto M (1985) The induced and intrinsic Finsler connections of a hypersurface and Finslerien projective geometry. J Math Kyoto Univ 25–1:107–144

    Article  MathSciNet  MATH  Google Scholar 

  6. Gupta MK, Pandey PN (2008) On hypersurface of a finsler space with a special metric. Acta Math Hung 120(1–2):165–177

    Article  MathSciNet  MATH  Google Scholar 

  7. Gupta MK, Pandey PN (2009) Hypersurfaces of conformally and h-conformally related Finsler spaces. Acta Math Hung 123(3):257–264

    Article  MathSciNet  MATH  Google Scholar 

  8. Gupta MK, Singh A, Pandey PN (2013) On a hypersurface of a Finsler space with randers change of matsumoto metric. Geometry 2013:1–6

    Article  MATH  Google Scholar 

  9. Gupta MK, Gupta AK (2016) Hypersurface of a Finsler Space subjected to an h-exponential change of metric. Int J Geom Methods Mod Phys 13(10):1–12

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Singh UP, Srivastava RK (1992) On a transformation associated with sets of n-fundamental forms of Finsler hypersurfaces. Indian J Pure Appl Math 23(5):325–332

    MathSciNet  MATH  Google Scholar 

  11. Kitayama M (2002) On Finslerian hypersurfaces given by \(\beta \)-changes. Balk J Geom Appl 7(2):49–55

    MathSciNet  MATH  Google Scholar 

  12. Matsumoto M (1986) Foundations of Finsler geometry and special Finsler spaces. Kaiseisha Press, Saikawa

    MATH  Google Scholar 

  13. Rapcsák A (1957) Eine neue Charakterisierung Finslerscher Räume Skalarer und konstanter Krümmung und projektiv-ebene Räume. Acta Math Acad Sci Hung 8:1–18

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. K. Gupta.

Additional information

Financialy supported by the University Grants Commission (UGC), Government of India through UGC-BSR Research Start-up-Grant.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gupta, M.K., Pandey, P.N. Hypersurface of a Finsler Space Subjected to a Kropina Change with an h-Vector. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 88, 241–246 (2018). https://doi.org/10.1007/s40010-017-0413-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40010-017-0413-2

Keywords

Mathematics Subject Classification

Navigation