Abstract

This paper presents a comprehensive investigation of the mappings establishing correspondences between the elliptic, parabolic, and hyperbolic upper half planes and the interior, boundary, and exterior of the projective unit circle in \(\mathbb{RP}^{2}\). Characterizations of Möbius-invariant cycle images are provided, and the definition of orthogonality for quadrics within the projective disk is introduced.

中文翻译：

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射影盘和 SL( $$\boldsymbol{3,\mathbb{R}}$$ ) 的作用：探索正交性

摘要

本文对建立椭圆、抛物线和双曲上半平面与\(\mathbb{RP}^{2}\)中射影单位圆的内部、边界和外部之间的对应关系的映射进行了全面的研究。提供了莫比乌斯不变循环图像的表征，并介绍了射影盘内二次曲面的正交性定义。