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SEIDEL’S CONJECTURES IN HYPERBOLIC 3-SPACE

  • OMAR CHAVEZ CUSSY
  • CARLOS H. GROSSIEmail author
Article

Abstract

We prove, in the case of hyperbolic 3-space, a couple of conjectures raised by J. J. Seidel in On the volume of a hyperbolic simplex, Stud. Sci. Math. Hung. 21 (1986), 243–249. Seidel’s first conjecture states that the volume of an ideal tetrahedron in hyperbolic 3-space is determined by (the permanent and the determinant of) a certain Gram matrix G of its vertices; Seidel’s fourth conjecture claims that the mentioned volume is a monotonic function of both the permanent and the determinant of G. A stronger form of the first conjecture is obtained: the permanent and the determinant of G are actually coordinates on the space of all ideal tetrahedra.

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References

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsICMC, University of São PauloSão CarlosBrazil

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