## Shapes of tetrahedra with prescribed cone angles

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- by Ahtziri González and Jorge L. López-López
- Conform. Geom. Dyn.
**15**(2011), 50-63 - DOI: https://doi.org/10.1090/S1088-4173-2011-00225-6
- Published electronically: June 7, 2011
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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.## References

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## Bibliographic Information

**Ahtziri González**- Affiliation: CIMAT, Mineral de Valenciana, C.P. 36240, Guanajuato, Gto., Mexico
- Email: ahtziri@cimat.mx
**Jorge L. López-López**- Affiliation: Facultad de Ciencias Físico-matemáticas, UMSNH, Ciudad Universitaria, C.P. 58040, Morelia, Mich., Mexico
- Email: jllopez@umich.mx
- 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”).
- © Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Conform. Geom. Dyn.
**15**(2011), 50-63 - MSC (2010): Primary 51M20; Secondary 58D17, 51M10, 51M25
- DOI: https://doi.org/10.1090/S1088-4173-2011-00225-6
- MathSciNet review: 2833472