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Exact solutions of the steady resistive three dimensional (3D)magnetohydrodynamics (MHD) equations in cylindrical coordinates for anincompressible plasma are presented. The solutions are translationallyinvariant along one direction and in general they describe a process ofreconnective annihilation in a curved current layer with non vanishing magneticfield. In the derivation of the solutions the ideal case with vanishingresistivity and electric field is considered first and then generalized toinclude the effects of finite electric field and resistivity. Particularattention is devoted to the analysis how the latter ones influence the presenceof singularities in the solutions. In this respect comparisons with the purelytwo-dimensional case are made and the resulting important differences arehighlighted. Finally, applications of the solutions for modeling an importantclass of solar flares are discussed.Comment: 14 pages, 4 figures. Accepted for publication in Physics of Plasma

Exact solutions for reconnective annihilation in magnetic configurations with three sources