On a system of fifth-order partial differential equations describing surfaces containing two families of circular arcs
On a system of fifth-order partial differential equations describing surfaces containing two families of circular arcs
复制标题
关于描述包含两个圆弧族的曲面的五阶偏微分方程组
DOI：
10.1080/17476933.2012.746967
复制
发表时间：
2013
影响因子：
0.9
通讯作者：
Kiyoomi Kataoka
中科院分区：
文献类型：
--
作者：
Y. Murakami and T. Iguchi;Kiyoomi Kataoka
设z =f（x，y）是一个在原点处的C5-曲面的芽，其中包含若干连续的圆弧族.例如，我们有一个通常的环面，有四个这样的家庭和R。布鲁姆的自行车与六个这样的家庭。我们引入了五阶非线性偏微分方程组，它完全描述了这样的表面芽。作为应用，我们得到了这类微分方程组解空间的解析性和有限维性。本文简要介绍了[Kataoka K，Takeuchi N.描述包含许多圆的曲面的五阶偏微分方程系统，UTMS 2012-10（东京大学数学科学研究生院预印本系列）]涉及包含两族圆弧的曲面。
Letz=f(x,y) be a germ of aC5-surface at the origin in ℝ3containing several continuous families of circular arcs. For examples, we have a usual torus with four such families and R. Blum's cyclide with six such families. We introduce the system of fifth-order nonlinear partial differential equations forfwhich describes such a surface germ completely. As applications, we obtain the analyticity off, and the finite dimensionality of the solution space of such a system of differential equations. We give a brief survey of [Kataoka K, Takeuchi N. A system of fifth-order partial differential equations describing a surface which contains many circles, UTMS 2012-10 (Preprint series of Graduate School of Mathematical Sciences, the University of Tokyo)] concerning surfaces containing two families of circular arcs.