International Journal of Pure and Applied Mathematics Volume 103 No. 4 2015, 613-624 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijpam.v103i4.2 P A ijpam.eu ON THE CONFORMAL CHANGE OF DOUGLAS SPACE OF SECOND KIND WITH CERTAIN (α, β)-METRICS Gauree Shanker 1 § , Deepti Choudhary 2 Department of Mathematics and Statistics Banasthali University Banasthali, Rajasthan, 304022, INDIA Abstract: The Douglas space of second kind with an (α, β)-metric was defined by I.Y. Lee [7]. In this paper, we prove that a Douglas space of second kind with an (α, β)-metric is conformally transformed to a Douglas space of second kind. Further, we find the conditions under which the conformal change of Finsler space with Matsumoto and generalized Kropina metric is of Douglas space of second kind. AMS Subject Classification: 53B40, 53C60 Key Words: conformal change, Douglas space, Douglas space of second kind, Matsumoto metric, generalized Kropina metric 1. Introduction It is well known that a Finsler space with (α, β)-metric is a Douglas space of second kind if the Douglas tensor D h ijk vanishes identically [3]. S. B´ acs´ o and Matsumoto [2] introduced the notion of a Finsler space with (α, β)-metric of Douglas type as a generalization of the Berwald space from the viewpoint of geodesic equations. Recently, I. Y. Lee [7] has studied Douglas space of second kind and he has find the conditions for a Finsler space with Matsumoto metric to be a Douglas space of second kind. Received: March 8, 2015 c  2015 Academic Publications, Ltd. url: www.acadpubl.eu § Correspondence author