论文标题
Minkowski平面中曲线的几何变形
Geometric deformations of curves in the Minkowski plane
论文作者
论文摘要
在本文中，我们将[17，18]中开发的方法扩展到Minkowski平面中的曲线。该方法提出了一种研究平面曲线变形的方法，考虑到它们的几何形状及其奇异性。我们详细介绍了所有局部曲线族中通常发生的所有局部现象。在每种情况下，我们都会获得变形曲线的几何形状，即有关拐点，顶点和灯泡点的信息。我们还获得了曲线在特定点上的进化/腐蚀性的行为，以及当曲线变形时可能发生的分叉。
In this paper, we extend the method developed in [17, 18] to curves in the Minkowski plane. The method proposes a way to study deformations of plane curves taking into consideration their geometry as well as their singularities. We deal in detail with all local phenomena that occur generically in 2-parameters families of curves. In each case, we obtain the geometry of the deformed curve, that is, information about inflections, vertices and lightlike points. We also obtain the behavior of the evolute/caustic of a curve at especial points and the bifurcations that can occur when the curve is deformed.
