A. D. Mednykh

Hyperbolic volumes of Fibonacci manifolds

A. Yu. Vesnin and A. D. Mednykh UDC 515.16 + 512.817.7 This article is devoted to the study of three-dimensional compact orientable hyperbolic manifolds connected with the Fibonacci groups. The Fibonacci groups F(2, m) = (Zl, z2,..., z,n : ziZi+l = zi+2, { mod m) were introduced by J. Conway [1]. The first natural question connected with these groups was whether they are finite or not [1]. It is known from [2-6] that the group F(2, m) is finite if and only if m = 1,2,3, 4,5, 7. Some algebraic generalizations of the groups

COVERING PROPERTIES OF SMALL VOLUME HYPERBOLIC 3-MANIFOLDS

Closed hyperbolic 3-manifolds obtained by Dehn surgeries on the Whitehead link yield interesting examples of manifolds of small volume. In the present paper these manifolds are described as 2-fold coverings of the 3-sphere branched over 3-bridge links. As a corollary, maximally symmetric -manifolds of small volume are obtained.

The volume of the Lambert cube in spherical space

AbstractThe Lambert cube Q(α, β, γ) is one of the simplest polyhedra. By definition, this is a combinatorial cube with dihedral angles α, β, and γ at three noncoplanar edges and with right angles at all other edges. The volume of the Lambert cube in hyperbolic space was obtained by R. Kellerhals (1989) in terms of the Lobachevskii function Λ(x). In the present paper, we find the volume of the Lambert cube in spherical space. It is expressed in terms of the function % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXguY9 % gCGievaerbd9wDYLwzYbWexLMBbXgBcf2CPn2qVrwzqf2zLnharyav % P1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC % 0xbbL8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yq % aqpepae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabe % qaamaaeaqbaaGcbaGaeqiTdqgcbaGae8hkaGIaeqySdeMae8hlaWIa % eqiUdeNae8xkaKIae8xpa0Zaa8qmaeaacyGGSbaBcqGGVbWBcqGGNb % WzcqGGOaakcqaIXaqmcqGHsislcyGGJbWycqGGVbWBcqGGZbWCcqaI % YaGmcqaHXoqycyGGJbWycqGGVbWBcqGGZbWCcqaIYaGmrmqr1ngBPr % gitLxBI9gBaGGbaiab+r8a0jabcMcaPaWcbaGaeqiUdehabaaccaGa % e0hWdaNaei4la8IaeGOmaidaniabgUIiYdGcdaWcaaqaaiabdsgaKj % ab+r8a0bqaaiGbcogaJjabc+gaVjabcohaZjabikdaYiab+r8a0baa % cqGGSaalaaa!70FD!

О формуле объема гиперболического тетраэдра@@@A formula for the volume of a hyperbolic tetrahedon

\delta (\alpha ,\theta ) = \int_\theta ^{\pi /2} {\log (1 - \cos 2\alpha \cos 2\tau )} \frac{{d\tau }} {{\cos 2\tau }},

On hyperbolic polyhedra arising as convex cores of quasi-Fuchsian punctured torus groups

which can be regarded as the spherical analog of the function % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXguY9 % gCGievaerbd9wDYLwzYbWexLMBbXgBcf2CPn2qVrwzqf2zLnharyav % P1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC % 0xbbL8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yq % aqpepae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabe % qaamaaeaqbaaGcbaGaeuiLdqecbaGae8hkaGIaeqySdeMae8hlaWIa % eqiUdeNae8xkaKIae8xpa0Jaeu4MdWKaeiikaGIaeqySdeMaey4kaS % IaeqiUdeNaeiykaKIaeyOeI0Iaeu4MdWKaeiikaGIaeqySdeMaeyOe % I0IaeqiUdeNaeiykaKIaeiOla4caaa!54BB!

Fibonacci manifolds as two-fold coverings of the three-dimensional sphere and the Meyerhoff-Neumann conjecture

\Delta (\alpha ,\theta ) = \Lambda (\alpha + \theta ) - \Lambda (\alpha - \theta ).