Revista de la
Unión Matemática Argentina
Canal surfaces with generalized 1-type Gauss map
Jinhua Qian, Mengfei Su, and Young Ho Kim
Volume 62, no. 1 (2021), pp. 199–211

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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.