É. Cartan  has originally introduced a Cartan space, which is considered as dual of Finsler space. H. Rund , F. Brickell  and others studied the relation between these two spaces. The theory of Hamilton spaces was introduced and studied by R. Miron ([8 , ). He proved that Cartan space is a particular case of Hamilton space. T. Igrashi (, ) introduced the notion of the (\alpha, \beta)-metric in Cartan spaces and obtained the metric tensor and the invariants \rho 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.
Cartan space, (\alpha, \beta)-metric, h-metrical d-connection, Conformally flat
NAGARAJA, H. G. (2007) "On Cartan Spaces with (\alpha, \beta)-metric," Turkish Journal of Mathematics: Vol. 31: No. 4, Article 3. Available at: https://journals.tubitak.gov.tr/math/vol31/iss4/3