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arXiv · 1111.3511

Polygons of the Lorentzian plane and spherical simplexes

François Fillastre
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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.

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François Fillastre. 2011-11-15. Polygons of the Lorentzian plane and spherical simplexes. https://arxiv.org/abs/1111.3511

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