平面上的星形仿射弹性曲线

Starlike Affine Elastic Curves On R^2

次仿射弹性曲线是全平方次仿射曲率泛函的临界点 .该文对平面上的星形仿射曲线进行了研究 ,用椭圆函数的方法解出了次仿射弹性曲线的次仿射曲率 ,并运用 Killing场和 sl(2 ,R)

The subaffine elastica is the critical point of the total squared subaffine curvature functional. In this paper, the starlike affine curve on the plane is dicussed. It solved the subaffine curvature of the subaffine elastica by using the elliptic function and completely solved the subaffine elastica by using the Killing field and the classification of the conjugate class of sl(2, R)