Geometry of the conics on the Minkowski plane

Abstract

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.