Minkowski平面上曲线的几何变形
Geometric deformations of curves in the Minkowski plane
摘要：
本文将文[17，18]中的方法推广到Minkowski平面上的曲线。该方法提出了一种方法来研究变形的平面曲线，考虑到他们的几何形状以及他们的奇异性。我们详细处理所有的局部现象，一般发生在2-参数曲线族。在每一种情况下，我们获得变形曲线的几何形状，即关于拐点、顶点和类光点的信息。我们还得到了曲线在特殊点处的渐屈线/焦散线的行为以及曲线变形时可能发生的分叉。
英文摘要：
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.
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。
