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Conformal Geometry and Dynamics

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Shapes of tetrahedra with prescribed cone angles

Authors: Ahtziri González and Jorge L. López-López
Journal: Conform. Geom. Dyn. 15 (2011), 50-63
MSC (2010): Primary 51M20; Secondary 58D17, 51M10, 51M25
Published electronically: June 7, 2011
MathSciNet review: 2833472
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Abstract: Given real numbers $4\pi >\theta _0\geq \theta _1\geq \theta _2\geq \theta _3>0$ so that $\sum _{j=0}^3\theta _j=4\pi$, we provide a detailed description of the space of flat metrics on the 2-sphere with 4 conical points of cone angles $\theta _0,\theta _1,\theta _2,\theta _3$, endowed with a geometric structure arising from the area function.

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Additional Information

Ahtziri González
Affiliation: CIMAT, Mineral de Valenciana, C.P. 36240, Guanajuato, Gto., Mexico

Jorge L. López-López
Affiliation: Facultad de Ciencias Físico-matemáticas, UMSNH, Ciudad Universitaria, C.P. 58040, Morelia, Mich., Mexico

Received by editor(s): December 7, 2010
Published electronically: June 7, 2011
Additional Notes: The study was partially supported by funding from the UMSNH (by means of a project of the CIC) and the SEP (by means of the Red Temática de Colaboración “Álgebra, topología y análisis”).
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.