可扩到任意赋范平面的正弦函数的几何性质
Geometric properties of a sine function extendable to arbitrary normed planes
摘要：
本文研究了正弦函数的度量推广，它可以推广到任意赋范平面上。我们得到了它的主要性质，并给出了Radon平面的一些特征。此外，我们证明了存在的角度测量，这是“良好的行为”相对于正弦是唯一可能的在欧几里德平面，我们还定义了一些新的常数，估计如何非氡或非欧几里德赋范平面可以。研究了保正弦自映射，给出了线性自映射的完整刻画。在最后一节中，我们展示了一个版本的正弦定律的氡飞机。
英文摘要：
In this paper we study a metric generalization of the sine function which can be extended to arbitrary normed planes. We derive its main properties and give also some characterizations of Radon planes. Furthermore, we prove that the existence of an angular measure which is "well-behaving" with respect to the sine is only possible in the Euclidean plane, and we also define some new constants that estimate how non-Radon or non-Euclidean a normed plane can be. Sine preserving self-mappings are studied, and a complete description of the linear ones is given. In the last section we exhibit a version of the Law of Sines for Radon planes.
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