Classification of generic spherical quadrilaterals
Complex Variables
2022-02-01 v2 Differential Geometry
Abstract
Generic spherical quadrilaterals are classified up to isometry. Condition of genericity consists in the requirement that the images of the sides under the developing map belong to four distinct circles which have no triple intersections. Under this condition, it is shown that the space of quadrilaterals with prescribed angles consists of finitely many open curves. Degeneration at the endpoints of these curves is also determined.
Keywords
Cite
@article{arxiv.2008.07999,
title = {Classification of generic spherical quadrilaterals},
author = {Andrei Gabrielov},
journal= {arXiv preprint arXiv:2008.07999},
year = {2022}
}
Comments
62 pages, 40 figures