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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 1850–1856 (Mi semr1040)  

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.

Funding Agency Grant Number
Russian Science Foundation 16-41-02006
This work was funded by the Russian Science Foundation (grant 16-41-02006).


DOI: https://doi.org/10.33048/semi.2018.15.149

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Bibliographic databases:

UDC: 515.162
MSC: 57M50,57M60
Received August 29, 2018, published December 30, 2018
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Citation: D. A. Derevnin, A. D. Mednykh, “Mirror symmetries of hyperbolic tetrahedral manifolds”, Sib. Èlektron. Mat. Izv., 15 (2018), 1850–1856

Citation in format AMSBIB
\Bibitem{DerMed18}
\by D.~A.~Derevnin, A.~D.~Mednykh
\paper Mirror symmetries of hyperbolic tetrahedral manifolds
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 1850--1856
\mathnet{http://mi.mathnet.ru/semr1040}
\crossref{https://doi.org/10.33048/semi.2018.15.149}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000454860200089}


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