有理单纯形问题的一种分析方法
An analytical approach to the Rational Simplex Problem
摘要：
在1973年，J. Cheeger和J. Simons提出了以下问题，这个问题仍然是开放的，被称为有理单形问题：给定球面三维空间中的一个测地线单形，使得它的所有内部二面角都是$π$的有理倍数，它的体积是三维球面体积的有理倍数吗？我们提出了一种分析方法，通过推导出一个功能$f(t)$，定义为一个初等函数的积分，这样，如果有一个合理的$t$，足够接近零，这样的值$f(t)$是一个无理数，然后理性单纯形问题的答案是否定的。
英文摘要：
In 1973, J. Cheeger and J. Simons raised the following question that still remains open and is known as the Rational Simplex Problem: Given a geodesic simplex in the spherical 3-space so that all of its interior dihedral angles are rational multiples of $π$, is it true that its volume is a rational multiple of the volume of the 3-sphere? We propose an analytical approach to the Rational Simplex Problem by deriving a function $f(t)$, defined as an integral of an elementary function, such that if there is a rational $t$, close enough to zero, such that the value $f(t)$ is an irrational number then the answer to the Rational Simplex Problem is negative.
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