Lightlike and ideal tetrahedra

Meusburger C, Scarinci C (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Geometriae Dedicata Springer Verlag (Germany)

Book Volume: 216

Journal Issue: 3

DOI: 10.1007/s10711-022-00687-6

Abstract

We give a unified description of tetrahedra with lightlike faces in 3d anti-de Sitter, de Sitter and Minkowski spaces and of their duals in 3d anti-de Sitter, hyperbolic and half-pipe spaces. We show that both types of tetrahedra are determined by a generalized cross-ratio with values in a commutative 2d real algebra that generalizes the complex numbers. Equivalently, tetrahedra with lightlike faces are determined by a pair of edge lengths and their duals by a pair of dihedral angles. We prove that the dual tetrahedra are precisely the generalized ideal tetrahedra introduced by Danciger. Finally, we compute the volumes of both types of tetrahedra as functions of their edge lengths or dihedral angles, obtaining generalizations of the Milnor-Lobachevsky volume formula of ideal hyperbolic tetrahedra.

Authors with CRIS profile

Cathérine Meusburger Professur für Mathematik (Darstellungstheorie und Mathematische Physik)

Involved external institutions

Ewha Womans University / 이화여자대학교 KR Korea, Republic of (KR)

How to cite

APA:

Meusburger, C., & Scarinci, C. (2022). Lightlike and ideal tetrahedra. Geometriae Dedicata, 216(3). https://dx.doi.org/10.1007/s10711-022-00687-6

MLA:

Meusburger, Cathérine, and Carlos Scarinci. "Lightlike and ideal tetrahedra." Geometriae Dedicata 216.3 (2022).

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