Abstract
There are many generalizations of Finsler geometry. A Finsler metric function is defined on the tangent bundle of a differentialble manifold with some assumptions. Especially, it is assumed to be positively homogeneous. The importance of a generalized metric has been emphasized by many authors ([2], [5], [7]). Some of them studied the non-homogeneous “metric” space ([1], [3], [4]). In [1], they investigated generalized Lagrangian space $(M, L)$ from the view point of Finsler spaces $(M^{*}, L^{*})$, where $M^{*}$ is the $(n+1)$-dimensional manifold and $L^{*}$ is positively homogeneous. The purpose of the present paper is to investigate the function without the assumption of homogeneity from another point of view.
Citation
Katsumi Okubo. "Differential geometry of generalized lagrangian functions." J. Math. Kyoto Univ. 31 (4) 1095 - 1103, 1991. https://doi.org/10.1215/kjm/1250519677
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