On the problem of non Berwaldian Landsberg spaces

In this paper, we study the long existence problem of non Berwaldian Landsberg spaces using the conformal transformation point of view. Under conformal transformation, the Berwald and Landesberg tensors are calculated in terms of the T-tensor. By giving examples, we show that under conformal transformation, there are Landsberg spaces with non-vanishing T-tensor. A necessary condition for a Landsberg space to be Berwaldian is given. Various special cases are studied. Cases in which the Landsberg spaces can not be Berwaldian are shown. Examples of non-Berwaldian landsberg (singular) spaces are given.