Hyperbolic and Euclidean Structures on Cone-Manifolds over Trefoil Knot with a Bridge
Nikolay AbrosimovRegional Scientific and Educational Mathematical Center, Tomsk State University, Tomsk, RussiaL. A. GrunwaldSobolev Institute of Mathematics, Novosibirsk, RussiaAlexander MednykhNovosibirsk State University, Novosibirsk, RussiaA. B. QutbaevNukus State Pedagogical Institute named after Ajiniyaz, Nukus, Republic of Karakalpakstan, UzbekistanB. VuongRegional Scientific and Educational Mathematical Center, Tomsk State University, Tomsk, Russia
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We study cone-manifolds whose singular set is the trefoil knot with a bridge and whose underlying space is the 3-dimensional sphere. We also establish necessary and sufficient conditions for the existence of such manifolds in both Euclidean and hyperbolic geometries, and derive explicit volume formulas in each case.
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