A class of real-analytic surfaces in the 3-Euclidean space
A class of real-analytic surfaces in the 3-Euclidean space
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3-欧几里得空间中的一类实解析曲面
DOI：
10.21099/tkbjm/1496164424
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发表时间：
2002
影响因子：
0.7
通讯作者：
N. Ando
中科院分区：
文献类型：
--
作者：
N. Ando
R3中的光滑曲面S称为平行曲线，如果R3中存在一个平面，使得在S的每个点上都存在一个平行于该平面的主方向。例如，平面、圆柱体和圆形球体是平行曲线。更一般地，旋转曲面也是平行曲线。本文的目的是研究主分布在实解析平行曲面上的性质，并对连通的、完全的、实解析的、嵌入的平行曲面进行分类。
A smooth surface S in R 3 is called parallel curved if there exists a plane in R 3 such that at each point of S, there exists a principal direction parallel to the plane. For example, a plane, a cylinder and a round sphere are parallel curved. More generally, a surface of revolution is also parallel curved. The purposes of this paper are to study the behavior of the principal distributions on a real-analytic, parallel curved surface and to classify the connected, complete, real-analytic, embedded, parallel curved surfaces.