PHYSICAL REVIEW D, cilt.100, sa.6, 2019 (SCI-Expanded)
We calculate the pair production rates for spin-1 or vector particles on spaces of the form M x R-1,R-1, with M corresponding to R-2 (flat), S-2 (positive curvature), and H-2 (negative curvature), with and without a background (chromo)magnetic field on M. Beyond highlighting the effects of curvature and background magnetic field, this is particularly interesting since vector particles are known to suffer from the Nielsen-Olesen instability, which can dramatically increase pair production rates. The form of this instability for S-2 and H-2 is obtained. We also give a brief discussion of how our results relate to ideas about confinement in non-Abelian theories.