## Tsukuba Journal of Mathematics

- Tsukuba J. Math.
- Volume 26, Number 2 (2002), 251-267.

### A class of real-analytic surfaces in the 3-Euclidean space

#### Abstract

A smooth surface $S$ in $\bf{R}^3$ is called *parallel curved* if there exists a plane in $\bf{R}^3$ 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.

#### Article information

**Source**

Tsukuba J. Math., Volume 26, Number 2 (2002), 251-267.

**Dates**

First available in Project Euclid: 30 May 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.tkbjm/1496164424

**Digital Object Identifier**

doi:10.21099/tkbjm/1496164424

**Mathematical Reviews number (MathSciNet)**

MR1940394

**Zentralblatt MATH identifier**

1029.53009

#### Citation

Ando, Naoya. A class of real-analytic surfaces in the 3-Euclidean space. Tsukuba J. Math. 26 (2002), no. 2, 251--267. doi:10.21099/tkbjm/1496164424. https://projecteuclid.org/euclid.tkbjm/1496164424