Einstein-Weyl-like conditions and causal structures in dimension three

Omid Makhmali (Polish Academy of Science, Warsaw)

Sep 14. 2021, 15:30 — 16:30

We generalize Einstein-Weyl conditions for three dimensional conformal structures to causal structures using their twistorial characterization. We define a causal structure as a field of null cones that are not necessarily quadratic. By augmenting a causal structure with a two parameter family of null surfaces one obtains a path geometry, which is an analogue of the projective structure on an Einstein-Weyl manifold. The resulting structure is in one to one correspondence with point equivalence classes of scalar third order ODEs. As a result of further natural integrability conditions, such structures are reduced to either classical Lorentzian Einstein-Weyl structures or special classes of half-flat Kähler metrics on the 4-dimensional space of paths.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Geometry for Higher Spin Gravity: Conformal Structures, PDEs, and Q-manifolds (Thematic Programme)
Xavier Bekaert (U Tours)
Andreas Cap (U of Vienna)
Stefan Fredenhagen (U of Vienna)
Maxim Grigoriev (Lebedev Inst. & Lomonosov Moscow SU)
Alexei Kotov (U Hradec Králové)