On S-3 like four-dimensional Finsler spaces

Abstract: In 1977, M. Matsumoto and R. Miron constructed an orthonormal frame for an $n$-dimensional Finsler space, called `Miron frame'. The present authors discussed four-dimensional Finsler spaces equipped with such frame. M. Matsumoto proved that in a three-dimensional Berwald space, all the main scalars are h-covariant constants and the h-connection vector vanishes. He also proved that in a three-dimensional Finsler space satisfying T-condition, all the main scalars are functions of position only and the v-connection vector vanishes. The purpose of the present paper is to generalize these results for an S-3 like four-dimensional Finsler space.

Keywords: Finsler space, Miron frame, Berwald space, T-condition, S-3 like space

Classification (MSC2000): 53B40

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