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arXiv 2008.009672020-08math.DG

通过接触几何与奇点研究演化曲面与演化隐式微分方程

Evolving Surfaces and Evolving Implicit Differential Equations Via Contact Geometry and Singularities

Ricardo Uribe-Vargas

备注：: 35 pages + 3 short appendices, 25 figures. Many results of this paper were exposed in the Singularity Theory Semester at Newton Institute (2000) and in a minicourse (Int. Conf. of Real and Complex Singularities Sao Carlos, 2002), where a preprint was distributed. This is a completely revamped version: shorter, clearer and includes several new results

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AI总结：

本文基于接触几何与奇点理论，研究了演化光滑曲面及演化隐式微分方程解的局部过渡现象，给出了抛物曲线、flecnodal 曲线和拐点曲线上不可避免的过渡列表。

摘要：

我们给出了在 R^3（或 RP^3）中演化光滑曲面的抛物曲线和 flecnodal 曲线配置上发生的不可避免局部现象（过渡）列表。我们还给出了演化隐式微分方程（IDE）解的拐点曲线上发生过渡的列表。我们的结果基于接触 3 空间中曲面的轮廓性质，这些投影的所有纤维均为 Legendrian。关键词：曲面、flecnodal 曲线、接触几何、隐式微分方程。

英文摘要：

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.

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