A formula for the volume of a hyperbolic tetrahedon

Derevnin, D. A.; Mednykh, Alexander

doi:10.1070/rm2005v060n02abeh000833

Cited by 27 publications

(24 citation statements)

References 6 publications

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“…In the coordinate patch U Γ the variety L γ is described by the generating function, which is a sum of dilogarithms, as follows from (69). This is to be contrasted with the results of [83], where the Gaudin eigenproblem in the case of half-integer ν k 's is solved by the trivial monodromy opers, which means, in the language of this paper, that the second brane corresponds to the unipotent monodromy flat connections.…”

Section: The Topological Branementioning

confidence: 74%

Darboux coordinates, Yang-Yang functional, and gauge theory

2014

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The moduli space of SL2 flat connections on a punctured Riemann surface Σ with the fixed conjugacy classes of the monodromies around the punctures is endowed with a system of holomorphic Darboux coordinates, in which the generating function of the variety of SL2-opers is identified with the universal part of the effective twisted superpotential of the corresponding four dimensional N = 2 supersymmetric theory subject to the two-dimensional Ω-deformation. This allows to give a definition of the Yang-Yang functionals for the quantum Hitchin system in terms of the classical geometry of the moduli space of local systems for the dual gauge group, and connect it to the instanton counting of the four dimensional gauge theories, in the rank one case.TCD MATH 11-05 HMI-11-04 IHES/P/11/16 ITEP-TH-16/11

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Section: The Topological Branementioning

confidence: 74%

Darboux coordinates, Yang-Yang functional, and gauge theory

2014

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“…We consider the adjoint matrix H = c ij i,j=1, 2,3,4 , where c ij = (−1) i+j M ij and M ij is the ijth minor of the matrix G. The proof of the following assertion can be found, for example, in [1]. Theorem 1.1.…”

Section: Preliminariesmentioning

confidence: 95%

Volumes of Convex Polyhedra in Hyperbolic Spaces

Krasnov

2015

J Math Sci

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“…Elementary formulas relating the dihedral angles and edge lengths of a tetrahedron in hyperbolic space are important in solving the classical problem of computation of the volume of a hyperbolic tetrahedron which was solved recently in [1][2][3][4]. Among the results of the present article, for instance, Theorem 2 ("The Law of Sines") we would single out as it reads classical.…”

Section: Introductionmentioning

confidence: 99%

“…Theorem 4 ("The Law of Cosines") appears to us to be a new or at least well forgotten result. Both theorems were used in [4] and [6] for calculating the volume of a symmetric hyperbolic tetrahedron. Basing on these theorems, we answer in the affirmative the question of Buser concerning the relation between the face areas and heights in a hyperbolic tetrahedron.…”

Section: Introductionmentioning

confidence: 99%