Indian J. Pure Appl. Math., 43(1): 37-48, February 2012 c Indian National Science Academy RANDERS CHANGE OF m th ROOT METRIC Asha Srivastava and Priya Arora Department of Mathematics, D.S.B. Campus, Kumaun University, Nainital, India e-mails: asriv 123@rediffmail.com, priya arora22march@yahoo.co.in (Received 1 August 2011; accepted 22 December 2011) The present paper deals with a Randers metric that has been derived after a particular β−change in the mth root metric. Various geometers such as [7], [9], [10] etc. have studied the mth root metric and its transformations. We have obtained some tensors and theorems holding the relation between the Finsler space equipped with the mth root metric and the one obtained after its Randers change. Key words : Finsler space, Randers space, mth root metric and β−change. 1. I NTRODUCTION A Finsler space F n is said to be equipped with (α, β) metric, if the metric function L(x, y) is positively homogeneous of degree one in α and β . Matsumoto [4] in 1971 introduced a particular transformation of Finsler metric α(x, y) defined as: L(x, y)= α(x, y)+ β (x, y), (1.1)