Constructions of Helicoidal Surfaces in Euclidean Space with Density

被引：13
|
作者：
Yoon, Dae Won [1 ,2 ]
Kim, Dong-Soo [3 ]
Kim, Young Ho [4 ]
Lee, Jae Won [1 ,2 ]
机构：
[1] Gyeongsang Natl Univ, Dept Math Educ, Jinju 52828, South Korea
[2] Gyeongsang Natl Univ, RINS, Jinju 52828, South Korea
[3] Chonnam Natl Univ, Dept Math, Gwangju 61186, South Korea
[4] Kyungpook Natl Univ, Dept Math, Daegu 41566, South Korea
来源：
SYMMETRY-BASEL | 2017年 / 9卷 / 09期
基金：
新加坡国家研究基金会;
关键词：
manifold with density; weighted curvature; helicoidal surface; ISOPERIMETRIC PROBLEM;
D O I：
10.3390/sym9090173
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：
Our principal goal is to study the prescribed curvature problem in a manifold with density. In particular, we consider the Euclidean 3-space R-3 with a positive density function e(phi), where phi = -x(2-) y(2), ( x, y, z) is an element of R-3 and construct all the helicoidal surfaces in the space by solving the second- order non- linear ordinary differential equation with the weighted Gaussian curvature and the mean curvature functions. As a result, we give a classification of weighted minimal helicoidal surfaces as well as examples of helicoidal surfaces with some weighted Gaussian curvature and mean curvature functions in the space.
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页数：9
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