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则曲线及二、三、四维空间中的仿射星形曲线。
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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 对于正则曲线的情形，我们发现了两个用于求解p -弹性曲线的结构方程的killing向量场并用积分将p -弹性曲线在一个柱面坐标系中表示出来，而对仿射星形曲线的情形，我们用积分方法解出了欧拉-拉格朗日方程，利用killing向量场及线性李代数s1 ( 2 ， r ) 、 s1 ( 3 ， r )和s1 ( 4 ， r )的分类将高阶结构方程降为一阶线性方程，因此我们用积分完全解出了中心仿射p -弹性曲线。
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