New Explicit Lorentzian Einstein-Weyl Structures in 3-Dimensions

Joël Merker, Universit&, Paweł Nurowski, #233, Paris-Saclay, France, Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Poland
2020 Symmetry, Integrability and Geometry: Methods and Applications  
On a 3D manifold, a Weyl geometry consists of pairs (g, A) = (metric, 1-form) modulo gauge g = e 2ϕ g, A = A + dϕ. In 1943, Cartan showed that every solution to the Einstein-Weyl equations R (µν) − 1 3 Rg µν = 0 comes from an appropriate 3D leaf space quotient of a 7D connection bundle associated with a 3 rd order ODE y = H(x, y, y , y ) modulo point transformations, provided 2 among 3 primary point invariants vanish
doi:10.3842/sigma.2020.056 fatcat:setzi3wngjcfzpnrskmrluvndq