2—Harmonic Curves Isometrially Immersed in a Surfaee

In this paper,the author proves the necessary and sufficient condition for the existence of 2-harmonically and isometrically immersed curves in a 2-dimensinonal surface N∪→IE^3.     

关于空间三次Bézier曲线的一个定理

Bezier曲线在计算机辅助几何设计中有着广泛的应用,其中三次曲线更为重要。本文就空间三次Bezier曲线的性质作一些讨论,并应用微分几何和向量分析的方法得到两个结果:这种曲线的参数一定不是弧长参数;没有重顶点的空间三次Bezier曲线是正则的,并且不含二重点和逗留点。这说明它的性质良好,易于控制。最后还给出了它的曲率和挠率的表达式。     

2-Harmonic Curves Isometrially Immersed in a Surface

In this paper,the author proves the necessary and sufficient condition for the existenceof 2-harmonically and isometrically immersed curves in a 2-dimensinonal surface N■IE~3.