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# On Cartan Spaces with Generalized (α,β)−metric

Authors

Gauree Shanker

Abstract

In 1933 E.Cartan [1] introduced a new space known as Cartan space. It is
considered as dual of Finsler space. H.Rund [4] , F.Brickell [2] and others studied the relation between these two spaces. The theory of Hamilton spaces was introduced and studied by R. Miron ([6] , [7]). T.Igrashi ([10] , [11]) introduced the notion of (α, β )-metric in Cartan spaces and obtained the metric tensor and the invariants ρ and σ which characterize the special classes of Cartan spaces with (α, β )-metric. Later on H.G.Nagaraja [3] studied Cartan spaces with (α, β)-metric in 2007. This paper deals with a study of Cartan spaces with Generalized (α, β )-metric admitting h-metrical d-connection. The conditions for these spaces to be locally Minkowaski and conformally flat have been obtained.

Keywords and Phrases : Cartan spaces, Generalized(α, β)-metric, h-metrical
d-connection, locally Minkowaski and conformally flat spaces
AMS Subject Classification : : 53C60, 53B40.

Received date : July 23, 2009

Accepted date: December 03, 2009

cited by: J.T.S. Vol. 4 (2010), pp.41-48