  A solution of the vortex type is given in a six-dimensional $SU(2)\times
U(1)$ pure gauge theory coupled to Einstein gravity in a compactified
background geometry. We construct the solution of an effective abelian Higgs
model in terms of dimensional reduction. The solution, however, has a
peculiarity in its physically relevant quantity, a deficit angle, which is
given as a function of the ratio of the gauge couplings of $SU(2)$ and $U(1)$.
The size of the extra space (sphere) is shown to vary with the distance from
the axis of the "string".
