Journal of applied mathematics & informatics

  • 제42권4호
  • /
  • Pages.879-897
  • /
  • 2024
  • /
  • 2734-1194(pISSN)
  • /
  • 2234-8417(eISSN)
한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지
DOI QR코드

DOI QR Code

THEORY OF HYPERSURFACES OF A FINSLER SPACE WITH THE GENERALIZED SQUARE METRIC

  • SONIA RANI (Department of Mathematics, School of Applied Sciences, Om Sterling Global University) ;
  • VINOD KUMAR (Department of Mathematics, School of Applied Sciences, Om Sterling Global University) ;
  • MOHAMMAD RAFEE (Department of Mathematics, School of Science, RIMT University)
  • 투고 : 2023.11.05
  • 심사 : 2024.02.27
  • 발행 : 2024.07.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

The emergence of generalized square metrics in Finsler geometry can be attributed to various classification concerning (𝛼, 𝛽)-metrics. They have excellent geometric properties in Finsler geometry. Within the scope of this research paper, we have conducted an investigation into the generalized square metric denoted as $F(x,y)=\frac{[{\alpha}(x,y)+{\beta}(x,y)]^{n+1}}{[{\alpha}(x,y)]^n}$, focusing specifically on its application to the Finslerian hypersurface. Furthermore, the classification and existence of first, second, and third kind of hyperplanes of the Finsler manifold has been established.

키워드

참고문헌

  1. V.K. Chaubey and A.K. Mishra, Hypersurfaces of a Finsler space with a special (α, β)-metric, J. Contemp. Mathemat. Anal. 52 (2017), 1-7.
  2. V.K. Chaubey and B.K. Tripathi, Finslerian Hypersurfaces of a Finsler Spaces with (α, β)-metric, Journal of Dynamical Systems and Geometric Theories 12 (2014), 19-27.
  3. G.C. Chaubey, G. Shanker and V. Pandey, On a hypersurface of a Finsler space with the special metric, ${\alpha}+\frac{{\beta}^{n+1}}{({\alpha}-{\beta}^n}$ , J.T.S. 7 (2013), 39-47.
  4. M. Kumar Gupta and S. Sharma, On Hypersurface of a Finsler space subjected to h-Matsumoto change, https://arxiv.org/pdf/2205.03520.pdf. 322 (2013), 401-409.
  5. I.Y. Lee, H.Y. Park and Y.D. Lee, On a hypersurface of a special Finsler space with a metric ${\alpha}+\frac{{\beta}^2}{{\alpha}}$, Korean J. Math. Sciences 322 (2013), 401-409.
  6. M. Kitayama, On Finslerian hypersurfaces given by β change, Balkan J. of Geometry and It's Applications 7 (2002), 49-55.
  7. John M. Lee, Introduction to Smooth Manifolds, Springer, New York, 2013.
  8. M. Matsumoto, Foundations of Finsler Geometry and Special Finsler Spaces, Kaiseisha Press, Otsu, Japan, 2013.
  9. M. Matsumoto, The induced and intrinsic Finsler connection of a hypersurface and Finslerian projective geometry, J. Math. Kyoto Univ. 25 (1985), 107-144.
  10. M. Matsumoto, Theory of Finsler spaces with (α, β)-metric, Rep. on Math. Phys. 31 (1992), 43-83.
  11. P.N. Panday and G.P. Yadav, Hypersurface of a Finsler space with Randers change of special (α, β)-metric, Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science 31 (2018), 195-206.
  12. M. Rafee and A. Kumar, and G.C. Chaubey, On the Hypersurface of a Finsler space with the square metric, Int. J. Pure. Appl. Math. 118 (2018), 723-733.
  13. G. Randers, On an Asymmetrical Metric in the Four-Space of General Relativity, Phys. Rev. 2 (1941), 195-199.
  14. G. Shanker and R. Yadav, On the hypersurface of a second approximate Matsumoto metric ${\alpha}+{\beta}\frac{{\beta}^2}{{\alpha}}+\frac{{\beta}^2}{{\alpha}^2}$, International J. of Contemp. Math. Sciences 7 (2012), 115-124.
  15. G. Shanker and Vijeta singh, On the hypersurface of a Finsler space with Randers change of generalized (α, β)-metric, International Journal of pure and applied Mathematics 105 (2015), 223-234.
  16. C. Shibata, On invariant tensors of β-change of Finsler metrics, J. Math. Kyoto Univ. 24 (1984), 163-188.
  17. H.S. Shukla and O.P. Pandey and A.K. Mishra, Hypersurface of a Finsler space with a special (α, β)-metric, South Asian 24 (1984), 163-188.
  18. U.P. Singh and Bindu Kumari, On a Matsumoto space, International Journal of pure and applied Mathematics 4 (2001), 521-531.
  19. Brijesh Kumar Tripathi, Hypersurfaces of a Finsler space with exponential form of (α, β)-metric, Annals of the University of Craiova-Mathematics and Computer Science Series 47 (2020), 132-140.
  20. H. Wosoughi, On a Hypersurface of a Special Finsler Space with an Exponential β α,-Metric, Int. J. Contemp. Math. Sciences 6 (2011), 1969-1980.