Spinorial representation of surfaces into 4-dimensional space forms

被引：13
|
作者：
Bayard, Pierre [1 ]
Lawn, Marie-Amelie [2 ,3 ]
Roth, Julien [4 ]
机构：
[1] Univ Michoacana, Inst Fis & Matemat, Morelia 58040, Michoacan, Mexico
[2] UT Austin, Austin, TX 78712 USA
[3] Univ Texas Austin, Dept Math, Austin, TX 78712 USA
[4] Univ Paris Est Marne la Vallee Cite Descartes, Lab Anal & Math Appl UMR 8050, F-77454 Champs Sur Marne 2, Marne La Vallee, France
来源：
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2013年 / 44卷 / 04期
关键词：
Dirac operator; Isometric immersions; Weierstrass representation; EIGENVALUES; BOUNDS;
D O I：
10.1007/s10455-013-9375-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we give a geometrically invariant spinorial representation of surfaces in four-dimensional space forms. In the Euclidean space, we obtain a representation formula which generalizes the Weierstrass representation formula of minimal surfaces. We also obtain as particular cases the spinorial characterizations of surfaces in and in given by Friedrich and by Morel.
引用
收藏
页码：433 / 453
页数：21
相关论文
共 50 条
  • [21] Biharmonic hypersurfaces in 4-dimensional space forms
    Balmus, Adina
    Montaldo, Stefano
    Oniciuc, Cezar
    MATHEMATISCHE NACHRICHTEN, 2010, 283 (12) : 1696 - 1705
  • [22] On translation surfaces in 4-dimensional Euclidean space
    Arslan, Kadri
    Bayram, Bengu
    Bulca, Betul
    Ozturk, Gunay
    ACTA ET COMMENTATIONES UNIVERSITATIS TARTUENSIS DE MATHEMATICA, 2016, 20 (02): : 123 - 133
  • [23] On biconservative surfaces in 4-dimensional Euclidean space
    Sen, Ruya Yegin
    Turgay, Nurettin Cenk
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 460 (02) : 565 - 581
  • [24] MINIMAL SURFACES OF 4-DIMENSIONAL EUCLIDEAN SPACE
    ROSCA, R
    COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1970, 270 (10): : 657 - &
  • [25] CLASSIFICATION THEOREMS FOR SPACE-LIKE SURFACES IN 4-DIMENSIONAL INDEFINITE SPACE FORMS WITH INDEX 2
    Chen, Bang-Yen
    Suceava, Bogdan D.
    TAIWANESE JOURNAL OF MATHEMATICS, 2011, 15 (02): : 523 - 541
  • [26] Spinorial Characterizations of Surfaces into 3-dimensional Pseudo-Riemannian Space Forms
    Marie-Amélie Lawn
    Julien Roth
    Mathematical Physics, Analysis and Geometry, 2011, 14 : 185 - 195
  • [27] Spinorial Characterizations of Surfaces into 3-dimensional Pseudo-Riemannian Space Forms
    Lawn, Marie-Amelie
    Roth, Julien
    MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY, 2011, 14 (03) : 185 - 195
  • [28] On biconservative hypersurfaces in 4-dimensional Riemannian space forms
    Turgay, Nurettin Cenk
    Upadhyay, Abhitosh
    MATHEMATISCHE NACHRICHTEN, 2019, 292 (04) : 905 - 921
  • [29] General rotational surfaces in the 4-dimensional Minkowski space
    Ganchev, Georgi
    Milousheva, Velichka
    TURKISH JOURNAL OF MATHEMATICS, 2014, 38 (05) : 883 - 895
  • [30] SOME REMARKS ON SURFACES IN 4-DIMENSIONAL EUCLIDEAN SPACE
    BURES, J
    CZECHOSLOVAK MATHEMATICAL JOURNAL, 1975, 25 (03) : 480 - 490
12345