黎曼几何基本定理的互易性
The Reciprocal of the Fundamental Theorem of Riemannian Geometry
摘要：
黎曼几何的基本定理被转化为解析的Christoffel符号。反演公式，此后被称为李嘉图公式，是在没有辅助假设的情况下获得的。尽管李嘉图公式可以在数学上给出完整的答案，但有人认为，解决方案应该只采取一个常数的保形因子。给出了从非参数化测地线中获取Christoffel符号的方法。因此，一个完整的框架，以获得度量的测量。该框架适用于重力几何性质实验的分析。
英文摘要：
The fundamental theorem of Riemannian geometry is inverted for analytic Christoffel symbols. The inversion formula, henceforth dubbed Ricardo's formula, is obtained without ancillary assumptions. Even though Ricardo's formula can mathematically give the full answer, it is argued that the solution should be taken only up to a constant conformal factor. A procedure to obtain the Christoffel symbols out of unparameterized geodesics is sketched. Thus, a complete framework to obtain the metric out of measurements is presented. The framework is suitable for analysis of experiments testing the geometrical nature of gravity.
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