%0 Journal Article
%T Local obstructions to a conformally invariant equation on M£¿bius surfaces
%A Matthew Randall
%J Mathematics
%D 2012
%I arXiv
%X On a M\"obius surface, as defined by D. Calderbank, we study a variant of the Einstein-Weyl (EW) equation which we call scalar-flat M\"obius EW (sf-MEW). This is a conformally invariant, finite type, overdetermined system of semi-linear partial differential equations. We derive local algebraic constraints for this equation to admit a solution and give local obstructions. In the generic case when a certain invariant of the M\"obius structure given by a symmetric tensor $M_{ab}$ is non-zero, the obstructions are given by resultants of 3 polynomial equations whose coefficients are conformal invariants of the M\"obius structure. The vanishing of the resultants is a necessary condition for there to be solutions to sf-MEW.
%U http://arxiv.org/abs/1211.2516v2