摘要
本文在文[1]基础上,讨论了E^3中曲面M为常平均曲率曲面的条件,得出:对于Gauss曲率k>0的曲面M,如果M上存在两个正交的单位向量v_1,v_2∈T_P(m),(m∈M),使得v_1H=0,v_2v_2H=0,且在αM上,v_2H=0,则在M上,H=常数.
In this paper, we have discussed the conditions of the surface with constant mean curvaturein E3, and have obtained:
Theorem, Let M: S→E3 be a surface.If M satisfies
i) K>0 on M; ii) There are two orthogonal unit tangent vector fields v1,v2, such that v1H = 0, v2v2H = 0; and iii) v2H = 0 on M.
Then H = constant on M.
