Polygons of the Lorentzian plane and spherical simplexes
Differential Geometry
2013-04-05 v2
Abstract
It is known that the space of convex polygons in the Euclidean plane with fixed normals, up to homotheties and translations, endowed with the area form, is isometric to a hyperbolic polyhedron. In this note we show a class of convex polygons in the Lorentzian plane such that their moduli space, if the normals are fixed and endowed with a suitable area, is isometric to a spherical polyhedron. These polygons have an infinite number of vertices, are space-like, contained in the future cone of the origin, and setwise invariant under the action of a linear isometry.
Keywords
Cite
@article{arxiv.1111.3511,
title = {Polygons of the Lorentzian plane and spherical simplexes},
author = {François Fillastre},
journal= {arXiv preprint arXiv:1111.3511},
year = {2013}
}
Comments
New text, title slightly changed