Existence and uniqueness for Legendre curves

被引：67

作者：

Fukunaga, Tomonori ^{[1
]}

Takahashi, Masatomo ^{[2
]}

机构：

[1] Hokkaido Univ, Dept Math, Sapporo, Hokkaido 0600810, Japan

[2] Muroran Inst Technol, Muroran, Hokkaido 0508585, Japan

来源：

JOURNAL OF GEOMETRY | 2013年 / 104卷 / 02期

关键词：

existence; uniqueness; Legendre curve; frontal; curvature of Legendre curve; congruent as Legendre curve;

D O I：

10.1007/s00022-013-0162-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a moving frame of a Legendre curve (or, a frontal) in the unit tangent bundle and define a pair of smooth functions of a Legendre curve like as the curvature of a regular plane curve. It is quite useful to analyse the Legendre curves. The existence and uniqueness for Legendre curves hold similarly to the case of regular plane curves. As an application, we consider contact between Legendre curves and the arc-length parameter of Legendre immersions in the unit tangent bundle.

引用

页码：297 / 307

页数：11

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