关于判别三维欧氏空间中一张曲面是否为凸曲面的问题,我们曾经给出过一些判别法^[1].而在工程设计上却有这样的一种判别法:沿着直角坐标系的三个坐标轴作一系列的平行平面与坐标轴相垂直,于是得到三组平行平面,在此之外再另取一平面,如果所有这些平面与曲面相截得出的都是凸曲线,那么就认为曲面是凸曲面.

In this paper,we prove the following.Theorem.A differentiable surface П in the 3-dimensional Euclidean space is a convex surfaee if and only if there exists such a point P∈π\∂π that.every plane S containing p satisfies the following condition:If there is a point q∈(S∩π)∩ int H(S∩π) where H(S∩π)is the convex hull of S∩π,then there exists a region G satisfying q∈G ⊂S∩π).