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ON GENERALIZED FINSLER STRUCTURES WITH A VANISHING hυ-TORSION

  • Published : 2004.03.01

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

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  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