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Cylindrically symmetric static manifolds are classified according to theirhomotheties and metrics. In each case the homothety vector fields and thecorresponding metrics are obtained explicitly by solving the homothetyequations. It turns out that these metrics admit homothety groups $H_m$, where$m=4,5,7,11$. This classification is then used to identify the cylindricallysymmetric static spaces admitting the local homotheties, which are globallyprohibited due to their topological construction. Einstein's field equationsare then used to identify the physical nature of the spaces thus obtained.Comment: 8 pages, no figur

Homotheties of cylindrically symmetric static manifolds and their global extension