A note on classification of proper homothetic vector fields in   Kantowski-Sachs and Bianchi type III Lorentzian manifolds
  A complete study of Kantowski-Sachs and Bianchi type III space-times according to their proper homothetic vector fields is given by using direct integration technique. Using the above mentioned technique we have shown that very special classes of the above space-times admit proper homothetic vector fields. The dimension of homothetic vector fields is five. 
Ghulam Shabbir and Fouzia Iqbal
gr-qc