论文标题
通过接触几何和奇异性不断发展的表面和不断发展的隐式微分方程
Evolving Surfaces and Evolving Implicit Differential Equations Via Contact Geometry and Singularities
论文作者
论文摘要
我们列出了在R^3（或RP^3）中不可避免的局部现象（过渡）的列表（或RP^3）中的抛物线曲线的构型。我们还介绍了在不断发展的隐式微分方程（IDE）的解决方案弯曲曲线上发生的过渡列表。我们的结果基于表面轮廓的特性（在触点3空间中），用于所有纤维是legendrian的投影。关键字：表面，漏动曲线，接触几何形状，隐式微分方程。
We present the list of unavoidable local phenomena (transitions) occurring on the configuration of the parabolic and flecnodal curves of evolving smooth surfaces in R^3 (or RP^3). We also present the list of transitions occurring on the curve of inflections of the solutions of evolving implicit differential equations (IDE). Our results are based on the properties of the contours of surfaces (in a contact 3-space) for projections all whose fibres are Legendrian. Keywords: Surface, flecnodal curve, contact geometry, implicit differential equations.
