Journal of the Mathematical Society of Japan

Contact of a regular surface in Euclidean 3-space with cylinders and cubic binary differential equations

Toshizumi FUKUI, Masaru HASEGAWA, and Kouichi NAKAGAWA

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Abstract

We investigate the contact types of a regular surface in the Euclidean 3-space $\mathbb{R}^3$ with right circular cylinders. We present the conditions for existence of cylinders with $A_1$, $A_2$, $A_3$, $A_4$, $A_5$, $D_4$, and $D_5$ contacts with a given surface. We also investigate the kernel field of $A_{\ge 3}$-contact cylinders on the surface. This is defined by a cubic binary differential equation and we classify singularity types of its flow in the generic context.

Article information

Source
J. Math. Soc. Japan Volume 69, Number 2 (2017), 819-847.

Dates
First available in Project Euclid: 20 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1492653648

Digital Object Identifier
doi:10.2969/jmsj/06920819

Subjects
Primary: 53A05: Surfaces in Euclidean space 53A60: Geometry of webs [See also 14C21, 20N05] 58K05: Critical points of functions and mappings 58C27

Keywords
contact with cylinders Monge cubic cylindrical directions

Citation

FUKUI, Toshizumi; HASEGAWA, Masaru; NAKAGAWA, Kouichi. Contact of a regular surface in Euclidean 3-space with cylinders and cubic binary differential equations. J. Math. Soc. Japan 69 (2017), no. 2, 819--847. doi:10.2969/jmsj/06920819. https://projecteuclid.org/euclid.jmsj/1492653648


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