대한수학회지 (Journal of the Korean Mathematical Society)

  • 제38권3호
  • /
  • Pages.503-521
  • /
  • 2001
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지

THE RANDER CHANGES OF FINSLER SPACES WITH ($\alpha,\beta$)-METRICS OF DOUGLAS TYPE

  • Park, Hong-Suh (Department of Mathematics, Yeungnam University) ;
  • Lee, Il-Yong (Department of Mathematics, Kyungsung University)
  • 발행 : 2001.05.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

A change of Finsler metric L(x,y)longrightarrowL(x,y) is called a Randers change of L, if L(x,y) = L(x,y) +$\rho$(x,y), where $\rho$(x,y) = $\rho$(sub)i(x)y(sup)i is a 1-form on a smooth manifold M(sup)n. Let us consider the special Randers change of Finsler metric LlongrightarrowL = L + $\beta$ by $\beta$. On the basis of this special Randers change, the purpose of the present paper is devoted to studying the conditions for Finsler space F(sup)n which are transformed by a special Randers change of Finsler spaces F(sup)n with ($\alpha$,$\beta$)-metrics of Douglas type to be also of Douglas type, and vice versa.

키워드

참고문헌

  1. The theory of sprays and Finsler spaces with applications in physics and biology P. L. Antonelli;R. S. Ingarden;M. Matsumoto
  2. Publ. Math. v.51 On the Finsler spaces of Douglas type. A generalization of the notion of the notion of Berwald space S. Bacso;M. Matsumoto
  3. Tensor(N. S.) v.57 Landsberg spaces of dimension two with (α ,β) -metric M. Hashiguchi;S. Hojo;M. Matsumoto
  4. Rep. Fac. Sici., Math. Phys. and Chem. v.13 Randers spaces with rectilinear geodesics M. Hashiguchi;Y. Ichijyo
  5. J. Math. v.14 On Finsler spaces with Randers metric and special forms of important tensors M. Matsumoto
  6. Foundations of Finsler Geometry and Special Finsler spaces
  7. Rep. Math. Phys. v.31 Theory of Finsler spaces with (α ,β) -metric
  8. Tensor(N. S.) v.60 Finsler spaces with (α ,β) -metric of Douglas type
  9. Tensor(N. S.) Projective Randers change of P-reducible Finsler spaces
  10. Comm. Korean Math. Soc. v.14 Finsler spaces with an approximate Matsumoto metric of Douglas type H. S. Park;E. S. Choi
  11. J. Korean Math. Soc. v.37 no.1 On the Landsberg spaces of dimension two with a special (α ,β) -metric H. S. Park;I. Y. Lee