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.
Citation
Naoya Ando. "A class of real-analytic surfaces in the 3-Euclidean space." Tsukuba J. Math. 26 (2) 251 - 267, December 2002. https://doi.org/10.21099/tkbjm/1496164424
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