  Exact solutions of the steady resistive three dimensional (3D)
magnetohydrodynamics (MHD) equations in cylindrical coordinates for an
incompressible plasma are presented. The solutions are translationally
invariant along one direction and in general they describe a process of
reconnective annihilation in a curved current layer with non vanishing magnetic
field. In the derivation of the solutions the ideal case with vanishing
resistivity and electric field is considered first and then generalized to
include the effects of finite electric field and resistivity. Particular
attention is devoted to the analysis how the latter ones influence the presence
of singularities in the solutions. In this respect comparisons with the purely
two-dimensional case are made and the resulting important differences are
highlighted. Finally, applications of the solutions for modeling an important
class of solar flares are discussed.
