Journal of the
Korean Mathematical Society JKMS

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

Keywords: generalized Finsler structures, $hv$-torsion, regular $(G,N)$-sturucture, Berwaldian $(G,N)$-sturucture, strongly Berwaldian structure, locally Minkowskian metric, $(L,N)$-structure, Rizza manifold, intrinsic $(G,N)$-structure

MSC numbers: 53B40