2011/11/15 by François Fillastre, Fillastre, François
Engineering · Mathematics · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Algebraic and Geometric Analysis #Mathematics and Applications #math.DG
paper · pdf · doi:10.48550/arxiv.1111.3511
New text, title slightly changed
arxiv created 2013/04/04 · arxiv updated 2013/04/05
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.