ON GENERALIZED FINSLER STRUCTURES WITH A VANISHING hυ-TORSION

Title & Authors
ON GENERALIZED FINSLER STRUCTURES WITH A VANISHING hυ-TORSION
Ichijyo, Yoshihiro; Lee, Il-Yong; Park, Hong-Suh;

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: $\small{{P^{i}}\;_{jk}\;=\;0}$ 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
generalized Finsler structures;hv-torsion;regular (G, N)-structure;Berwaldian (G, N)-structure;strongly Berwaldian structure;locally Min-kowskian metric;(L, N)-structure;Rizza manifold;intrinsic (G, N)-structure;
Language
English
Cited by
1.
Horizontal Laplace Operator in Real Finsler Vector Bundles, Acta Mathematica Scientia, 2008, 28, 1, 128
2.
Formulas of Gauss-Ostrogradskii Type on Real Finsler Manifolds, Acta Mathematica Scientia, 2008, 28, 2, 383
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