隐式奇异曲面上的抛物曲线、脊曲线和亚抛物曲线

IF 0.5 4区数学 Q3 MATHEMATICS Osaka Journal of Mathematics 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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来源期刊

Osaka Journal of Mathematics 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Osaka Journal of Mathematics is published quarterly by the joint editorship of the Department of Mathematics, Graduate School of Science, Osaka University, and the Department of Mathematics, Faculty of Science, Osaka City University and the Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University with the cooperation of the Department of Mathematical Sciences, Faculty of Engineering Science, Osaka University. The Journal is devoted entirely to the publication of original works in pure and applied mathematics.