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<p>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.</p>

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Hyperbolic and Euclidean Structures on Cone-Manifolds over Trefoil Knot with a Bridge

  • 期刊论文

  • 发表日期：

    2025年5月1日

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  • N. V. Abrosimov,
  • L. A. Grunwald,
  • A. D. Mednykh,
  • A. B. Qutbaev,
  • B. Vuong

摘要

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.