On cartan spaces with $(alpha,beta )$- metric

Abstract

E. Cartan [2] has originally introduced a Cartan space, which is considered as dual of Finsler space. H. Rund [10], F. Brickell [1] and others studied the relation between these two spaces. The theory of Hamilton spaces was introduced and studied by R. Miron ([8] , [9]). He proved that Cartan space is a particular case of Hamilton space. T. Igrashi ([5], [6]) introduced the notion of the $(alpha,beta )$ - metric in Cartan spaces and obtained the metric tensor and the invariants ρ and r which characterize the special classes of Cartan spaces with $(alpha,beta )$-metric. This paper presents a study of Cartan spaces with $(alpha,beta )$-metric admitting h-metrical d-connection. We prove the conditions for these spaces to be locally Minkowski and conformally flat.