  We study a 6-dimensional brane world model with an abelian string residing in
the two extra dimensions. We study both static as well as inflating branes and
find analytic solutions for the case of trivial matter fields in the bulk. Next
to singular space-times, we also find solutions which are regular including
cigar-like universes as well as solutions with periodic metric functions. These
latter solutions arise if in a singular space-time a static brane is replaced
by an inflating brane. We determine the pattern of generic solutions for
positive, negative and zero bulk cosmological constant.
