Constant mean curvature one surfaces in hyperbolic 3-space using the Bianchi-Calo method

被引：7
作者：
De Lima, LL [1 ]
Roitman, P [1 ]
机构：
[1] Univ Fed Ceara, Dept Matemat, BR-60455760 Fortaleza, Ceara, Brazil
来源：
ANAIS DA ACADEMIA BRASILEIRA DE CIENCIAS | 2002年 / 74卷 / 01期
关键词：
constant mean curvature one surfaces; congruence of spheres; rolling of surfaces; Weierstrass representation;
D O I：
10.1590/S0001-37652002000100002
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In this note we present a method for constructing constant mean curvature on surfaces in hyperbolic 3-space in terms of holomorphic data first introduced in Bianchi's Lezioni di Geometria Differenziale of 1927, therefore predating by many years the modem approaches due to Bryant, Small and others. Besides its obvious historical interest, this note aims to complement Bianchi's analysis by deriving explicit formulae for CMC-1 surfaces and comparing the various approaches encountered in the literature.
引用
收藏
页码：19 / 24
页数：6
相关论文
共 6 条
[1]  
BIANCHI L, 1927, LEZIONI GEOMETRIA DI
[2]  
BRYANT RL, 1987, ASTERISQUE, P321
[3]  
CALO B, 1899, ANN MATEMATICA, V4
[4]  
Lawson H. B, 1980, Mathematics Lecture Series, V9
[5]   SURFACES OF CONSTANT MEAN-CURVATURE-1 IN H-3 AND ALGEBRAIC-CURVES ON A QUADRIC [J].
SMALL, AJ .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 122 (04) :1211-1220
[6]   COMPLETE-SURFACES OF CONSTANT MEAN CURVATURE-1 IN THE HYPERBOLIC 3-SPACE [J].
UMEHARA, M ;
YAMADA, K .
ANNALS OF MATHEMATICS, 1993, 137 (03) :611-638
1