广义旋转超曲面的法线刻画

Characterizing hypersurfaces of generalized rotation through its normal lines

得到了伪欧氏空间里的超曲面是广义旋转超曲面一个充要条件,即存在一条直线与曲面的每一条法线相交或平行,特别的,所有法线都交于一点的超曲面只能是广义球面或它的一部分．作为上述结论的特殊情形,三维欧氏空间中的旋转曲面有同样结论．

In pseudo- Euclidean space , a hypersurface is generalized rotation one, which is either a hypersurface can be expressed as graph locally or a cylinder, is sufficient and necessary that there exist a straight line either intersects or parallels all its normal lines. More over, the only hypersurface whose all normal lines have a point is just a generalized hyper - sphere or part of it. As a special case, in 3 - dimensional Euclidean space, a surface is rotational if and only if there exist a straight line either intersects or parallels all its normal lines. The only surface whose all normal lines have a common point is just a sphere or part of it.