On S—3 Like Five-Dimensional Finsler Spaces

Abstract

In 1977, M. Matsumoto and R. Miron [1] constructed an orthonormal frame for an n−dimensional Finsler space called ‘Miron frame’. M. Matsumoto [2,3] 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 function of position only and the v−connection vector vanishes [2, 4]. M. K. Gupta and P. N. Pandey [5] proved that in an S− like four-dimensional Berwald space satisfying T−condition, all the main scalars are constants and the h− and v−connection vector vanish. The purpose of the present paper is to generalize these results for an S − 3 like five-dimensional Finsler space.