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Canal surfaces with generalized 1-type Gauss map
Volume 62, no. 1
(2021),
pp. 199–211
https://doi.org/10.33044/revuma.1685
Abstract
This work considers a kind of classification of canal surfaces in terms of
their Gauss map $\mathbb{G}$ in Euclidean 3-space. We introduce the notion of
generalized 1-type Gauss map for a submanifold that satisfies $\Delta
\mathbb{G}=f\mathbb{G}+gC$, where $\Delta$ is the Laplace operator, $C$ is a
constant vector, and $(f, g)$ are non-zero smooth functions. First of all, we
show that the Gauss map of any surface of revolution with unit speed profile
curve in Euclidean 3-space is of generalized 1-type. At the same time, the
canal surfaces with generalized 1-type Gauss map are discussed.
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Published by the Unión Matemática Argentina |
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