Existence and uniqueness for Legendre curves
Existence and uniqueness for Legendre curves
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DOI：
10.1007/s00022-013-0162-6
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发表时间：
2012-12
影响因子：
0.6
通讯作者：
Tomonori Fukunaga;Masatomo Takahashi
中科院分区：
文献类型：
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作者：
Tomonori Fukunaga;Masatomo Takahashi
我们给出单位切丛中勒让德曲线（或锋面）的移动框架，并像正则平面曲线的曲率一样定义一对勒让德曲线的平滑函数。分析勒让德曲线非常有用。勒让德曲线的存在性和唯一性与正则平面曲线的情况类似。作为一个应用，我们考虑勒让德曲线与单位切丛中勒让德浸没的弧长参数之间的接触。
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.