2017/02/27 by Jean-Philippe Burelle, Virginie Charette, Burelle, Jean-Philippe +5
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DG #math.SG
paper · pdf · doi:10.48550/arxiv.1702.08414
-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
arxiv created 2019/09/16 · arxiv updated 2019/09/17
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.