English

Einstein tori and crooked surfaces

Differential Geometry 2019-09-17 v2 Symplectic Geometry

Abstract

In hyperbolic space, the angle of intersection and distance classify pairs of totally geodesic hyperplanes. A similar algebraic invariant classifies pairs of hyperplanes in the Einstein universe. In dimension 3, symplectic splittings of a 4-dimensional real symplectic vector space model Einstein hyperplanes and the invariant is a determinant. The classification contributes to a complete disjointness criterion for crooked surfaces in the 3-dimensional Einstein universe.

Keywords

Cite

@article{arxiv.1702.08414,
  title  = {Einstein tori and crooked surfaces},
  author = {Jean-Philippe Burelle and Virginie Charette and Dominik Francoeur and William Goldman},
  journal= {arXiv preprint arXiv:1702.08414},
  year   = {2019}
}

Comments

-Corrected typos -Added definitions and details to AdS crooked planes section -Clarified choice of representatives for Plucker coordinates in Section 4 -Added a figure of a crooked surface

R2 v1 2026-06-22T18:29:44.951Z