洛伦兹平面的多边形与球面单形
Polygons of the Lorentzian plane and spherical simplexes
摘要：
已知欧氏平面上的凸多边形的空间具有固定的法线，直到同构和平移，赋予面积形式，是等距于双曲多面体。本文证明了洛伦兹平面上的一类凸多边形，如果法线固定并赋予适当的面积，则它们的模空间与球面多面体等距。这些多边形有无穷多个顶点，是类空间的，包含在原点的未来圆锥中，并且在线性等距的作用下是setwise不变的。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
