Lines of principal curvature on canal surfaces in R3

被引：12
|
作者：
Garcia, Ronaldo
Llibre, Jaume
Sotomayor, Jorge
机构：
[1] Univ Fed Goias, Inst Matemat & Estatist, BR-74001970 Goiania, Go, Brazil
[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain
[3] Univ Sao Paulo, Inst Matemat & Estatist, BR-05508090 Sao Paulo, Brazil
来源：
ANAIS DA ACADEMIA BRASILEIRA DE CIENCIAS | 2006年 / 78卷 / 03期
关键词：
Riccati equation; principal curvature lines; canal surfaces;
D O I：
10.1590/S0001-37652006000300002
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 paper are determined the principal curvatures and principal curvature lines on canal surfaces which are the envelopes of families of spheres with variable radius and centers moving along a closed regular curve in R-3. By means of a connection of the differential equations for these curvature lines and real Riccati equations, it is established that canal surfaces have at most two isolated periodic principal lines. Examples of canal surfaces with two simple and one double periodic principal lines are given.
引用
收藏
页码：405 / 415
页数：11
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