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ON THE SPECIAL FINSLER METRIC

  • Lee, Nan-Y
  • Published : 2003.08.01

Abstract

Given a Riemannian manifold (M, $\alpha$) with an almost Hermitian structure f and a non-vanishing covariant vector field b, consider the generalized Randers metric $L\;=\;{\alpha}+{\beta}$, where $\beta$ is a special singular Riemannian metric defined by b and f. This metric L is called an (a, b, f)-metric. We compute the inverse and the determinant of the fundamental tensor ($g_{ij}$) of an (a, b, f)-metric. Then we determine the maximal domain D of $TM{\backslash}O$ for an (a, b, f)-manifold where a y-local Finsler structure L is defined. And then we show that any (a, b, f)-manifold is quasi-C-reducible and find a condition under which an (a, b, f)-manifold is C-reducible.

Keywords

Finsler metric;generalized Randers metric;(a, b, f)-metric;Rizza manifold;C-reducible

References

  1. Tensor(N.S.) v.37 Almost Hermitian Finsler manifolds Y.Ichiiyo
  2. Foundations of Finsler geometry and special Finsler spaces M.Matsumoto
  3. Rep. Fac. Sci. Kagoshima Univ. Math. Phys. Chem v.29 On(a, b, f)-metrics Ⅱ
  4. Rep. Fac. Sci. Kagoshima Univ. Math. Phys. Chem v.28 On(a, b, f)-metrics Y.Ichiiyo;M.Hashiguchi
  5. Graduate Texts in Mathematics An introduction to Riemannian-Finsler geometry D.Bao;S.S.Chern;Z.Shen
  6. Tensor(N.S.) v.24 On C-reducible Finsler spaces

Cited by

  1. An almost paracontact structure on a Rizza manifold vol.349, pp.11-12, 2011, https://doi.org/10.1016/j.crma.2011.06.005