• Journal of the Korean Mathematical Society
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• v.41 no.2
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• pp.369-378
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• 2004

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.

• East Asian mathematical journal
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• v.16 no.2
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• pp.339-354
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• 2000

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.327-340
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• 2003

We are devoted to dealing with the conformal theory of a Rizza manifold with a generalized Finsler metric $G_{ij}$ (x,y) and a new conformal invariant non-linear connection $M^{i}$ $_{j}$ (x,y) constructed from the generalized Cern's non-linear connection $N^{i}$ $_{j}$ (x,y) and almost complex structure $f^{i}$ $_{j}$ (x). First, we find a conformal invariant connection ( $M_{j}$ $^{i}$ $_{k}$ , $M^{i}$ $_{j}$ , $C_{j}$ $^{i}$ $_{k}$ ) and conformal invariant tensors. Next, the nearly Kaehlerian (G, M)-structures under conformal change in a Rizza manifold are investigate.

• Journal of the Korean Mathematical Society
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• v.49 no.6
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• pp.1229-1257
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• 2012

We study the relation between an R-Cartan structure ${\alpha}$ an an (I, J, K)-generalized Finsler structure ${\omega}$ on a 3-manifold ${\Sigma}$ showing the difficulty in finding a general transformation that maps ${\alpha}$ to ${\omega}$. In some particular cases, the mapping can be uniquely determined by geometrical conditions. Moreover, we are led in this way to a negative answer to our conjecture in [12].