Reductions of Gauss-Codazzi Equations

被引：2

作者：

Conte, Robert

Grundland, A. Michel

机构：

[1] Univ Paris Saclay, Ctr Math & Leurs Applicat, Ecole Normale Super Cachan, CNRS, Cachan, France

[2] Univ Hong Kong, Hong Kong, Hong Kong, Peoples R China

[3] Univ Montreal, Montreal, PQ H3C 3J7, Canada

[4] Univ Quebec Trois Rivieres, Trois Rivieres, PQ, Canada

来源：

STUDIES IN APPLIED MATHEMATICS | 2016年 / 137卷 / 03期

关键词：

DIFFERENTIAL-EQUATIONS; SURFACES; 2ND-ORDER;

D O I：

10.1111/sapm.12121

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that conformally parameterized surfaces in Euclidean space R3(c) of curvature c admit a symmetry reduction of their Gauss-Codazzi equations whose general solution is expressed with the sixth Painleve function. Moreover, it is shown that the two known solutions of this type (Bonnet 1867, Bobenko etal. 1997) can be recovered by such a reduction.

引用

页码：306 / 327

页数：22

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