R^3中主曲率满足1/(k_1)-1/(k_2)=c的旋转曲面

The Rotation Surfaces with Principal Curvature Satisfying 1/(k_1)-1/(k_2) =c in R^3

研究欧氏空间R^3中主曲率满足1/k_1-1/k_2=c的旋转Weingarten曲面,其中c∈R为常数,k_1,k_2是曲面上一点处的两个主曲率.我们对满足这种关系的旋转Weingarten曲面进行了分类,并且发现这些曲面在每一类中彼此都是平行的.

We study Weingarten surfaces in Euclidean 3-space that satisfy a Weingarten relation of 1/κ_1—1/κ_2=c,where c∈R andκ_1,κ_2 denote the principal curvature at each point of the surface.We have classified all the rotational Weingarten surfaces that satisfies the relationship of above,and we find that all these surfaces are parallel each other.