Classification of non conformally flat cylindrically symmetric non static space-times according to their proper conformal motions

In this paper we considered the most general form of non conformally flat cylindrically symmetric non-static space-times to study proper conformal motions using direct integration technique. We have shown that very special classes for cylindrically symmetric space-times admit proper conformal motions. This classification also covers non-static and static plane symmetric space-times. In [9] it was claimed that non conformally flat plane symmetric static space-times do not admit proper conformal motion. Here it is also shown that static and non static plane symmetric space-times admit proper conformal motions. We also discuss the Lie algebra in each case.