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

共 50 条

[1] GAUSS-CODAZZI EQUATIONS
JACOBOWI.HJ
[J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 21 (07): : A642 - A642
[2] Integration of the Gauss-Codazzi equations
Zakharov, VE
[J]. THEORETICAL AND MATHEMATICAL PHYSICS, 2001, 128 (01) : 946 - 956
[3] KAEHLER GAUSS-CODAZZI EQUATIONS
JACOBOWITZ, H
[J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 22 (01): : A206 - A206
[4] S-CONNECTION AND GAUSS-CODAZZI EQUATIONS
UPADHYAY, MD
AWASTHI, CP
[J]. ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1975, 26 (1-2): : 75 - 80
[5] Gauss-Codazzi Equations for Thin Films and Nanotubes Containing Defects
Derezin, Svyatoslav
[J]. SHELL-LIKE STRUCTURES: NON-CLASSICAL THEORIES AND APPLICATIONS, 2011, 15 : 531 - 548
[6] Gauss-Codazzi equations for generic surfaces: Equivalence to the DS linear problem with constraint, linearizability and reductions
Konopelchenko, BG
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1997, 30 (13): : L437 - L441
[7] Dependence of the Gauss-Codazzi equations and the Ricci equation of Lorentz surfaces
Chen, Bang-Yen
[J]. PUBLICATIONES MATHEMATICAE-DEBRECEN, 2009, 74 (3-4): : 341 - 349
[8] Gauss-Codazzi thermodynamics on the timelike screen
Piazza, Federico
[J]. PHYSICAL REVIEW D, 2010, 82 (08):
[9] GAUSS-CODAZZI EQUATIONS AND FIELD EQUATIONS FOR A SPECIAL CASE OF NULL HYPERSURFACES IN THEORY OF GRAVITATION
SOKOLOWSKI, LM
[J]. ACTA PHYSICA POLONICA B, 1975, 6 (04): : 529 - 536
[10] GENERALISATION OF GAUSS-CODAZZI EQUATIONS FOR BERWALDS CURVATURE TENSORS IN A HYPERSURFACE OF A FINSLER SPACE
SINHA, RS
[J]. TENSOR, 1969, 20 (01): : 13 - &

← 1 2 3 4 5 →