Mirror symmetries of hyperbolic tetrahedral manifolds

D. A. Derevnin ; A. D. Mednykh

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1850-1856.

Résumé

Let $\Lambda$ be the group generated by reflections in faces of a Coxeter tetrahedron in the hyperbolic space $\mathbb{H}^3$. A tetrahedral manifold is a hyperbolic manifold $\mathcal{M}=\mathbb{H}^3/\Gamma$ uniformized by a torsion free subgroup $\Gamma$ of the group $\Lambda$. By a mirror symmetry we mean an orientation reversing isometry of the manifold acting by reflection. The aim of the paper to investigate mirror symmetries of the tetrahedral manifolds.

Détail

Keywords: hyperbolic space, isometry group, hyperbolic manifolds.
Mots-clés : automorphism group

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