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Einstein tori and crooked surfaces

  • Jean-Philippe Burelle EMAIL logo , Virginie Charette , Dominik Francoeur and William M. Goldman
From the journal Advances in Geometry


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.

Funding statement: Burelle, Charette and Francoeur gratefully acknowledge partial support from the Natural Sciences and Engineering Research Council of Canada. We also gratefully acknowledge partial support from the US National Science Foundation, in particular grants DMS 1406281 and, especially DMS 1107367 “Research Networks in the Mathematical Sciences: Geometric structures And Representation varieties” (the GEAR Network)

  1. Communicated by: T. Leistner


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Received: 2018-09-05
Accepted: 2019-08-28
Published Online: 2021-03-11
Published in Print: 2021-04-27

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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