隐式奇异曲面上的抛物曲线、脊曲线和亚抛物曲线

Pub Date : 2017-10-01 DOI:10.18910/67009

Masaru Hasegawa

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引用次数: 2

摘要

我们研究了由等价于A1-奇异性的光滑函数R-定义的隐式曲面上的抛物曲线、脊曲线和次抛物曲线。为了研究脊曲线和次抛物线，我们给出了隐式曲面的局部参数化，并通过参数化展示了主曲率和方向的渐近行为。我们还在附录中介绍了隐式曲面上的高度和距离平方函数。

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PARABOLIC, RIDGE AND SUB-PARABOLIC CURVES ON IMPLICIT SURFACES WITH SINGULARITIES

We study parabolic, ridge and sub-parabolic curves on implicit surfaces defined by smooth functions R-equivalent to A1 -singularity. To investigate ridge and sub-parabolic curves, we present the local parameterizations of the implicit surfaces, and we show the asymptotic behavior of the principal curvatures and directions by using the parameterization. We also present height and distance squared functions on implicit surfaces in the appendix.

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