BOUR'S THEOREM IN 4-DIMENSIONAL EUCLIDEAN SPACE

被引：10

作者：

Doan The Hieu ^{[1
]}

Nguyen Ngoc Thang ^{[1
]}

机构：

[1] Hue Univ, Coll Educ, 32 Le Loi, Hue, Vietnam

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2017年 / 54卷 / 06期

关键词：

Bour's theorem; helicoidal surface; surface of revolution; Gauss map; minimal surface; MINKOWSKI; 3-SPACE; MAP;

D O I：

10.4134/BKMS.b160766

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we generalize 3-dimensional Bour's Theorem to the case of 4-dimension. We proved that a helicoidal surface in R-4 is isometric to a family of surfaces of revolution in R-4 in such a way that helices on the helicoidal surface correspond to parallel circles on the surfaces of revolution. Moreover, if the surfaces are required further to have the same Gauss map, then they are hyperplanar and minimal. Parametrizations for such minimal surfaces are given explicitly.

引用

页码：2081 / 2089

页数：9

共 11 条

[1]

Bour E., 1862, J LECOLE POLYTECH, VXXXIX Cahier, P1

[2]

Bozkurt Z., 2012, MATH AETERNA, V2, P701

[3] ON THE BOUR'S THEOREM WITH RESPECT TO CONFORMAL MAP IN MINKOWSKI SPACE E-1(3) [J].