TY - JOUR

T1 - Local obstructions to a conformally invariant equation on Möbius surfaces

AU - Randall, Matthew

PY - 2014/3

Y1 - 2014/3

N2 - On a Möbius surface, as defined in [1], we study a variant of the Einstein-Weyl (EW) equation which we call scalar-flat Möbius 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 Möbius structure given by a symmetric tensor M a b is non-zero, the obstructions are given by resultants of 3 polynomial equations whose coefficients are conformal invariants of the Möbius structure. The vanishing of the resultants is a necessary condition for there to be solutions to sf-MEW.

AB - On a Möbius surface, as defined in [1], we study a variant of the Einstein-Weyl (EW) equation which we call scalar-flat Möbius 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 Möbius structure given by a symmetric tensor M a b is non-zero, the obstructions are given by resultants of 3 polynomial equations whose coefficients are conformal invariants of the Möbius structure. The vanishing of the resultants is a necessary condition for there to be solutions to sf-MEW.

KW - Conformal differential geometry

KW - Invariance and symmetry properties

KW - Overdetermined systems with variable coefficients

UR - http://www.scopus.com/inward/record.url?scp=84895903328&partnerID=8YFLogxK

U2 - 10.1016/j.difgeo.2013.10.014

DO - 10.1016/j.difgeo.2013.10.014

M3 - Article

SN - 0926-2245

VL - 33

SP - 112

EP - 122

JO - Differential Geometry and its Application

JF - Differential Geometry and its Application

ER -