Canal surfaces with generalized 1-type Gauss map

Authors

  • Jinhua Qian Department of Mathematics, Northeastern University, Shenyang 110004, People’s Republic of China
  • Mengfei Su Department of Mathematics, Northeastern University, Shenyang 110004, People’s Republic of China
  • Youngho Kim Department of Mathematics, Kyungpook National University, Daegu 41566, Korea

DOI:

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

2021-05-31

Issue

Vol. 62 No. 1 (2021)

Section

Article

License

Copyright (c) 2021 Youngho Kim, Jinhua Qian, Mengfei Su

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