RULED SURFACES WITH VANISHING 2ND GAUSSIAN CURVATURE

被引：26

作者：

BLAIR, DE ^{[1
]}

KOUFOGIORGOS, T ^{[1
]}

机构：

[1] UNIV IOANNINA,DEPT MATH,GR-45110 IOANNINA,GREECE

来源：

MONATSHEFTE FUR MATHEMATIK | 1992年 / 113卷 / 03期

关键词：

D O I：

10.1007/BF01641765

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a surface free of points of vanishing Gaussian curvature in Euclidean space the second Gaussian curvature is defined formally. It is first pointed out that a minimal surface has vanishing second Gaussian curvature but that a surface with vanishing second Gaussian curvature need not be minimal. Ruled surfaces for which a linear combination of the second Gaussian curvature and the mean curvature is constant along the rulings are then studied. In particular the only ruled surface in Euclidean space with vanishing second Gaussian curvature is a piece of a helicoid.

引用

页码：177 / 181

页数：5