Shapes of tetrahedra with prescribed cone angles

Author:

González Ahtziri,López-López Jorge

Abstract

Given real numbers 4 π > θ 0 θ 1 θ 2 θ 3 > 0 4\pi >\theta _0\geq \theta _1\geq \theta _2\geq \theta _3>0 so that j = 0 3 θ j = 4 π \sum _{j=0}^3\theta _j=4\pi , we provide a detailed description of the space of flat metrics on the 2-sphere with 4 conical points of cone angles θ 0 , θ 1 , θ 2 , θ 3 \theta _0,\theta _1,\theta _2,\theta _3 , endowed with a geometric structure arising from the area function.

Publisher

American Mathematical Society (AMS)

Subject

Geometry and Topology

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