发表机构
School of Mathematics and Statistics, Hunan First Normal University; School of Mathematics and Statistics, Wuhan University; International Center for Mathematical Research (BICMR), Beijing (Peking) University（湖南第一师范学院数学与统计学院; 武汉大学数学与统计学院; 北京大学国际数学研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究三维流形上 Thurston 双曲球面堆积的刚性，证明其由组合标量曲率局部确定且具有无穷小刚性，主要工具包括容许空间刻画、二面角变分公式及恒等式。
AI 中文摘要
本文研究三维流形上 Thurston 双曲球面堆积的刚性。我们证明了 Thurston 双曲球面堆积由组合标量曲率局部确定。我们进一步证明了无穷小刚性，即 Thurston 双曲球面堆积在保持组合 Ricci 曲率不变的情况下不能变形。主要工具包括 Thurston 双曲球面堆积的容许空间的一个刻画、四面体二面角的变分公式，以及由 Thurston 双曲球面堆积生成的四面体中二面角变化的一个恒等式。
英文摘要
In this paper, we study the rigidity of Thurston's hyperbolic sphere packings on 3-dimensional manifolds. We prove that Thurston's hyperbolic sphere packing is locally determined by combinatorial scalar curvature. We further prove the infinitesimal rigidity that Thurston's hyperbolic sphere packing can not be deformed while keeping the combinatorial Ricci curvature fixed. The main tools include a characterization of the admissible space of Thurston's hyperbolic sphere packings, a variational formula for the dihedral angles of a tetrahedron and an identity for the variations of dihedral angles in a tetrahedron generated by Thurston's hyperbolic sphere packings.
Comments29 pages
