论文标题
超球三角学和相应的椭圆功能
Hyperspherical Trigonometry and Corresponding Elliptic Functions
论文作者
论文摘要
我们使用多维矢量产物开发了多维欧几里得空间中超球三角学的基本公式，以及它们转化为椭圆函数的身份。我们表明，在4维空间中嵌入的3个球体上功能的基本添加公式导致椭圆函数的添加公式，与代数曲线相关，这些曲线具有两个不同的模量。我们将这些公式应用于多维Euler Top的情况，并使用它们提供了与双椭圆模型的链接。
We develop the basic formulae of hyperspherical trigonometry in multidimensional Euclidean space, using multidimensional vector products, and their conversion to identities for elliptic functions. We show that the basic addition formulae for functions on the 3-sphere embedded in 4-dimensional space lead to addition formulae for elliptic functions, associated with algebraic curves, which have two distinct moduli. We give an application of these formulae to the cases of a multidimensional Euler top, using them to provide a link to the Double Elliptic model.
