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A complete study of Kantowski-Sachs and Bianchi type III space-timesaccording to their proper homothetic vector fields is given by using directintegration technique. Using the above mentioned technique we have shown thatvery special classes of the above space-times admit proper homothetic vectorfields. The dimension of homothetic vector fields is five.

A note on classification of proper homothetic vector fields in Kantowski-Sachs and Bianchi type III Lorentzian manifolds