Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ON GENERALIZED FINSLER STRUCTURES WITH A VANISHING hυ-TORSION

  • Published : 2004.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

A canonical Finsler connection Nr is defined by a generalized Finsler structure called a (G, N)-structure, where G is a generalized Finsler metric and N is a nonlinear connection given in a differentiable manifold, respectively. If NT is linear, then the(G, N)-structure has a linearity in a sense and is called Berwaldian. In the present paper, we discuss what it means that NT is with a vanishing hv-torsion: ${P^{i}}\;_{jk}\;=\;0$ and introduce the notion of a stronger type for linearity of a (G, N)-structure. For important examples, we finally investigate the cases of a Finsler manifold and a Rizza manifold.

Keywords

References

  1. An Stiint. Univ. Al.I. Cuza Iasi v.30 On generalized Finsler spaces M.Hashiguchi
  2. Rev. Mat. Univ. Parma(4) v.14 Finsler metrics on almost complex manifolds Y.Ichijyo
  3. J. Math. Tokushima Univ. Conformally flat Finsler structures M.Hashiguchi
  4. Res. Bull. Toku-shima Bunri Univ. v.57 Kaehlerian Finsler manifolds of Chern type M.Hashiguchi
  5. Res. Bull. Toku-shima Bunri Univ. v.59 On the flatness of generalized Finsler manifolds adn Kaehlerian Finsler manifolds of Chern type M.Hashiguchi
  6. Res. Bull. Toku-shima Bunri Univ. v.61 On geneeralized Finsler structures I Y.Ichijyo;M.Hashiguchi
  7. J. Math. Kyoto Univ. v.23 Metrical Finsler structures and metrical Finsler connections R.Miron https://doi.org/10.1215/kjm/1250521554
  8. Foundations of Finsler geometry and special Finsler spaces M.Matsumoto
  9. J. Math. Kyoto Univ. v.22 Minkowskian product of Finsler spaces and Berwald connection T.Okada https://doi.org/10.1215/kjm/1250521819
  10. Atti Acad. Naz. Lincei Rend. v.33 Strutture di Finsler sulle varieta quasi complesse G.B.Rizza

Cited by

  1. Formulas of Gauss-Ostrogradskii Type on Real Finsler Manifolds vol.28, pp.2, 2008, https://doi.org/10.1016/S0252-9602(08)60040-5
  2. Horizontal Laplace Operator in Real Finsler Vector Bundles vol.28, pp.1, 2008, https://doi.org/10.1016/S0252-9602(08)60013-2