Einstein tori and crooked surfaces

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.

-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