Proper Homothetic Vector Fields on Three Dimensional Lorentzian Manifold of Circularly Symmetric Static Spacetimes

In this paper we are interested to investigate proper homothetic vector fields on a three dimensional Lorentzian manifold. For the purpose, Lie derivative of three dimensional circular symmetric static metric has been taken along the vector field. The obtained six coupled partial differential equations are then solved by using direct integration technique. It is investigated that the above metric does not admit proper homothetic vector field .The homothetic vector fields in the above metric are the Killing vector fields.