- 【數(shù)學(xué)】正弧。
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regular curve中文什么意思
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- This paper deals with the regular curves in a riemannian manifold with constant sectional curvature and the affine starlike curves in r2 , r3 and r4
本文研究了具有常截面曲率的黎曼流形中的正則曲線及二、三、四維空間中的仿射星形曲線。 - For the regular curves , we find two killing fields for the purpose of integrating the structural equations of the p - elastic curves and express the p - elastica by quadratures in a system of cylindrical coordinates . for the star - like affine curves , we solve the euler - lagrange equation by quadratures and reduced the higher order structure equation to a first order linear system by using killing field and the classification of linear lie algebra sl ( 2 , r ) , sl ( 3 , r ) and sl ( 4 , r ) . we solve the centroaffine p - elastica completely by quadratures
對于正則曲線的情形，我們發(fā)現(xiàn)了兩個用于求解p -彈性曲線的結(jié)構(gòu)方程的killing向量場并用積分將p -彈性曲線在一個柱面坐標系中表示出來，而對仿射星形曲線的情形，我們用積分方法解出了歐拉-拉格朗日方程，利用killing向量場及線性李代數(shù)s1 ( 2 ， r ) 、 s1 ( 3 ， r )和s1 ( 4 ， r )的分類將高階結(jié)構(gòu)方程降為一階線性方程，因此我們用積分完全解出了中心仿射p -彈性曲線。