高阶Schl{ä}fli公式及其应用II .向量值微分关系
Higher Schl{ä}fli Formulas and Applications II. Vector-valued differential relations
摘要：
经典的Schläfli公式，以及[SS 03]中给出的“更高”的类似物，是多面体（可以是欧几里得的，球面的或双曲的）在一阶变形下的不同尺寸的面的体积和“曲率”变化之间的关系。我们在这里描述的类似物的那些公式是矢量值，而不是标量。一些后果如下，例如约束锥奇点可以出现时，常曲率流形之间的锥流形变形。
英文摘要：
The classical Schläfli formula, and its ``higher'' analogs given in [SS03], are relations between the variations of the volumes and ``curvatures'' of faces of different dimensions of a polyhedra (which can be Euclidean, spherical or hyperbolic) under a first-order deformation. We describe here analogs of those formulas which are vector-valued rather than scalar. Some consequences follow, for instance constraints on where cone singularities can appear when a constant curvature manifold is deformed among cone-manifolds.
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。
