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arXiv 2103.07709math.GThep-thmath-phmath.MP
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超双曲余弦定律:同一公式不同内容

Super Hyperbolic Law of Cosines: same formula with different content

Robert Penner

摘要:

我们利用Minkowski超几何导出了超双曲平面中的余弦和正弦定律,得到了与经典情形相同的公式,但明显地涉及到余弦和角度正弦的不同表达式,其中包含了大量的费米子修正。在进一步类比的经典情况下,我们应用这些结果表明,两个平行的超测地线,这不是超平行承认一个独特的共同正交超测地线,我们简要介绍了方面的小学超数理论,导致一个前瞻性的模拟高斯产品的二次型。

英文摘要:

We derive the Laws of Cosines and Sines in the super hyperbolic plane using Minkowski supergeometry and find the identical formulae to the classical case, but remarkably involving different expressions for cosines and sines of angles which include substantial fermionic corrections. In further analogy to the classical case, we apply these results to show that two parallel supergeodesics which are not ultraparallel admit a unique common orthogonal supergeodesic, and we briefly describe aspects of elementary supernumber theory, leading to a prospective analogue of the Gauss product of quadratic forms.

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。

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