Omid Makhmali (CTP):Einstein-Weyl-like conditions, ruled affine spheres, and causal structures in 3D
Channel: Centrum Fizyki Teoretycznej PAN
Date: 2021-09-14

Omid Makhmali (CTP PAS).
Einstein-Weyl-like conditions, ruled affine spheres, and causal structures in 3D.
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.

GRIEG collaboration project: SCREAM workshop 2021.