Minkowski平面上二次曲线的几何
Geometry of the conics on the Minkowski plane
摘要：
欧氏空间中的二次曲线以其几何美和模拟现实生活中的几种现象的能力而闻名。通常在考虑半黎曼流形中的二次曲线时，我们想到的方程和图形是二次欧几里德方程。例如，一个圆总是被认为是一个封闭的曲线。我们研究了半黎曼闵可夫斯基时空中二次曲线的几何，并用欧几里得的眼光解释了每个方程。通过定义二次曲线的扩展几何完备性，我们将证明二次曲线的圆锥完备性可以通过欧几里德镜像来改变。
英文摘要：
Conics in the Euclidean space have been known for their geometrical beauty and also for their power to model several phenomena in real life. It usually happens that when thinking about the conics in a semi-Riemannian manifold, the equations and the graphs that come to mind are those of the quadratic Euclidean equations. For example, a circle is always perceived like a closed curve. We study the geometry of the conics in the semi-Riemannian Minkowski spacetime, and interpret each equation with Euclidean eyes. By defining an extended geometric completeness for conics, we will show that the conic completeness of conics can be changed through a Euclidean mirror.
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。
