  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.

Differential Geometry