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Geometry and topology
Mirror symmetries of hyperbolic tetrahedral manifolds
D. A. Derevnina, A. D. Mednykhbc a Industrial University of Tyumen,
Lunacharskogo, 1,
625001, Tyumen, Russia
b Sobolev Institute of Mathematics,
pr. Koptyuga, 4,
630090, Novosibirsk, Russia
c Novosibirsk State University,
Pirogova, 2,
630090, Novosibirsk, Russia
Abstract:
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.
Keywords:
hyperbolic space, isometry group, automorphism group, hyperbolic manifolds.
Received August 29, 2018, published December 30, 2018
Citation:
D. A. Derevnin, A. D. Mednykh, “Mirror symmetries of hyperbolic tetrahedral manifolds”, Sib. Èlektron. Mat. Izv., 15 (2018), 1850–1856
Linking options:
https://www.mathnet.ru/eng/semr1040 https://www.mathnet.ru/eng/semr/v15/p1850
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Abstract page: | 300 | Full-text PDF : | 145 | References: | 31 |
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