二面角球面曲面的模空间与测度叶状结构
Moduli Space of Dihedral Spherical Surfaces and Measured Foliations
AI总结：
本文研究二面角球面曲面，通过定义一对横向测度叶状结构来完全刻画该类曲面，并引入几何分解与形变方法，最终确定给定锥角和拓扑类型下模空间的维数。
摘要：
锥球面是常曲率为一且具有有限个锥奇点的可定向黎曼曲面。这些曲面中的一个子集，称为二面角曲面，其特征是其单值群显著保持三维欧氏空间中单位二维球面上的一对对径点。在每个二面角曲面上，我们定义一对横向测度叶状结构，它们反过来全面地刻画了原始的二面角曲面。此外，我们引入了一系列针对二面角曲面的几何分解与形变。作为一个实际应用，我们确定了在给定锥角和拓扑类型下二面角曲面模空间的维数。该维数作为决定这些曲面等距类的独立几何参数数量的指标。
英文摘要：
Cone spherical surfaces are orientable Riemannian surfaces with constant curvature one and a finite set of conical singularities. A subset of these surfaces, referred to as dihedral surfaces, is characterized by their monodromy groups, which notably preserve a pair of antipodal points on the unit two-sphere within three-dimensional Euclidean space. On each dihedral surface, we define a pair of transverse measured foliations that, in turn, comprehensively characterize the original dihedral surface. Furthermore, we introduce a variety of geometric decompositions and deformations specific to dihedral surfaces. As a practical application, we ascertain the dimension of the moduli space for dihedral surfaces given specified cone angles and topological types. This dimension acts as an indicator of the independent geometric parameters that determine the isometric classes of these surfaces.
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。
