Discrete special isothermic surfaces

被引：5

作者：

Burstall, F. ^{[1
]}

Hertrich-Jeromin, U. ^{[2
]}

Rossman, W. ^{[3
]}

Santos, S. ^{[4
]}

机构：

[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England

[2] Vienna Univ Technol, A-1040 Vienna, Austria

[3] Kobe Univ, Dept Math, Kobe, Hyogo 6578501, Japan

[4] Univ Lisbon, Dept Matemat, CMAF, P-1749016 Lisbon, Portugal

来源：

GEOMETRIAE DEDICATA | 2015年 / 174卷 / 01期

关键词：

Isothermic surface; Darboux transformation; Lawson correspondence; Backlund transformation; Polynomial conserved quantity; Constant mean curvature;

D O I：

10.1007/s10711-014-0001-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We discuss special isothermic nets of type , a new class of discrete isothermic nets, generalizing isothermic nets with constant mean curvature in spaceforms. In the case these are the discrete analogues of Bianchi's special isothermic surfaces that can be regarded as the origin of the rich transformation theory of isothermic surfaces. Accordingly, special isothermic nets come with Backlund transformations and a Lawson correspondence. The notion of complementary nets naturally occurs and sheds further light on the relation between geometry and integrability.

引用

页码：1 / 11

页数：11

共 50 条

[1] Discrete special isothermic surfaces
F. Burstall
U. Hertrich-Jeromin
W. Rossman
S. Santos
Geometriae Dedicata, 2015, 174 : 1 - 11
[2] Discrete isothermic surfaces
Bobenko, A
Pinkall, U
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1996, 475 : 187 - 208
[3] Discrete Koenigs Nets and Discrete Isothermic Surfaces
Bobenko, Alexander I.
Suris, Yuri B.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2009, 2009 (11) : 1976 - 2012
[4] Semi-Discrete Isothermic Surfaces
Mueller, Christian
Wallner, Johannes
RESULTS IN MATHEMATICS, 2013, 63 (3-4) : 1395 - 1407
[5] Semi-Discrete Isothermic Surfaces
Christian Müller
Johannes Wallner
Results in Mathematics, 2013, 63 : 1395 - 1407
[6] Semi-discrete isothermic surfaces
F. Burstall
U. Hertrich-Jeromin
C. Müller
W. Rossman
Geometriae Dedicata, 2016, 183 : 43 - 58
[7] Semi-discrete isothermic surfaces
Burstall, F.
Hertrich-Jeromin, U.
Mueller, C.
Rossman, W.
GEOMETRIAE DEDICATA, 2016, 183 (01) : 43 - 58
[8] Special isothermic surfaces of type d
Burstall, F. E.
Santos, S. D.
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2012, 85 : 571 - 591
[9] Discrete Lorentz surfaces and s-embeddings I: Isothermic surfaces
Affolter, Niklas christoph
Dellinger, Felix
Mueller, Christian
Polly, Denis
Smeenk, Nina
JOURNAL OF GEOMETRY AND PHYSICS, 2025, 213
[10] Isothermic surfaces
Thybaut, A
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES, 1900, 131 : 932 - 935

← 1 2 3 4 5 →