空间曲线存在定理与黎卡提方程

如所知,空间曲线存在唯一性基本定理是很重要的。在这篇文章里,我们介绍Frenet-Serret方程与黎卡提方程之间的一种有趣联系,对证明存在定理和由自然方程求曲线可供参考。

The Existence Theorem of Space Curves and Riccati Equation

As known, the fundamental existence and uniqueness theorem for space curves is very important. In this paper, we introduse an interesting connection between the Frenet - Serret equations and the Riccati equation, being referable to prove the existence theorem and to find the curve according to its natural equation.