Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Finslerian Hypersurface and Generalized β-Conformal Change of Finsler Metric

  • Tiwari, Shiv Kumar (Department of Mathematics, K. S. Saket Post Graduate College) ;
  • Rai, Anamika (Department of Mathematics, K. S. Saket Post Graduate College)
  • Received : 2015.03.11
  • Accepted : 2018.02.13
  • Published : 2018.12.23
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Abstract

In the present paper, we have studied the Finslerian hypersurfaces and generalized ${\beta}$-conformal change of Finsler metric. The relations between the Finslerian hypersurface and the other which is Finslerian hypersurface given by generalized ${\beta}$-conformal change have been obtained. We have also proved that generalized ${\beta}$-conformal change makes three types of hypersurfaces invariant under certain conditions.

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References

  1. M. Hashiguchi, On conformal transformations of Finsler metrics, J. Math. Kyoto Univ., 16(1976), 25-50. https://doi.org/10.1215/kjm/1250522956
  2. H. Izumi, Conformal transformations of Finsler spaces I, Tensor (N.S.), 31(1977), 33-41.
  3. H. Izumi, Conformal transformations of Finsler spaces II, Tensor (N.S.), 34(1980), 337-359.
  4. S. Kikuchi, On the theory of subspace in a Finsler space, Tensor (N.S.), 2(1952), 67-69.
  5. M. Kitayama, Finslerian hypersurfaces and metric transformations, Tensor (N.S.), 60(1998), 171-178.
  6. M. Kitayama, Geometry of transformations of Finsler metrics, Hokkaido University of Education, Kushiro Campus, Japan, 2000.
  7. M. S. Knebelman, Conformal geometry of generalized metric spaces, Proc. Nat. Acad. Sci. USA, 15(1929), 376-379. https://doi.org/10.1073/pnas.15.4.376
  8. M. Matsumoto, The induced and intrinsic Finsler connections of a hypersurface and Finslerian projective geometry, J. Math. Kyoto Univ., 25(1985), 107-144. https://doi.org/10.1215/kjm/1250521161
  9. A. Moor, Finsler raume von identischer torsion, Acta Sci. Math., 34(1973), 279-288.
  10. B. N. Prasad and Bindu Kumari, The ${\beta}$-change of Finsler metric and imbedding classes of their tangent spaces, Tensor (N.S.), 74(2013), 48-59.
  11. B. N. Prasad and Gauri Shanker, Finslerian hypersurfaces and ${\beta}$-change of Finsler metric, Acta Cienc. Indica Math., 35(3)(2009), 1055-1061.
  12. C. Shibata, On invariant tensors of ${\beta}$-change of Finsler metrics, J. Math. Kyoto Univ., 24(1984), 163-188. https://doi.org/10.1215/kjm/1250521391
  13. S. K. Tiwari and Anamika Rai, The generalized ${\beta}$-change of Finsler metric, International J. Contemp. Math. Sci., 9(2014), 695-702. https://doi.org/10.12988/ijcms.2014.410111