扩展双曲空间中线段的中点坐标

IF 0.4 Q4 MATHEMATICS International Electronic Journal of Geometry Pub Date : 2023-04-18 DOI:10.36890/iejg.1270550

L. Romakina

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引用次数: 0

摘要

在本文中，我们发现了线类型的一个解析特征，并导出了在第一类框架中的扩展双曲空间$H^3$中椭圆、双曲和抛物段的中点和拟中点坐标的计算公式。在Cayley\，--\，Klein投影模型中，我们认为空间$H^3$是一个固定有椭圆二次曲面$\gamma$的投影三维空间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Coordinates of the Midpoint of a Segment in an Extended Hyperbolic Space

In this article, we find an analytical characteristic of the type of a line and derive the formulae for calculating the coordinates of the midpoints and quasi-midpoints of elliptic, hyperbolic, and parabolic segments in an extended hyperbolic space $H^3$ in the frame of the first type. The space $H^3$ we consider in the Cayley\,--\,Klein projective model as a projective three-dimensional space with an oval quadric $\gamma$ fixed in it.

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