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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.