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 -