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Geometry of trefoil cone-manifold. (English) Zbl 1363.51005

Summary: In this paper we prove that the trefoil knot cone manifold \(\mathcal{T} (\alpha)\) with cone angle \(\alpha\) is spherical for \(\pi/3 < \alpha < 5\pi/3\). We show also that its spherical volume is given by the formula Vol\((\mathcal{T} (\alpha))=(3\alpha - \pi)^2/12\).

MSC:

51M10 Hyperbolic and elliptic geometries (general) and generalizations
51M25 Length, area and volume in real or complex geometry
26B15 Integration of real functions of several variables: length, area, volume
57M25 Knots and links in the \(3\)-sphere (MSC2010)
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