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Surfaces of Revolution and Canal Surfaces with Generalized Cheng–Yau 1-Type Gauss Maps

Author

Listed:
  • Jinhua Qian

    (Department of Mathematics, Northeastern University, Shenyang 110004, China)

  • Xueshan Fu

    (Department of Mathematics, Jeju National University, Jeju 63243, Korea)

  • Xueqian Tian

    (Department of Mathematics, Northeastern University, Shenyang 110004, China)

  • Young Ho Kim

    (Department of Mathematics, Kyungpook National University, Daegu 41566, Korea)

Abstract

In the present work, the notion of generalized Cheng–Yau 1-type Gauss map is proposed, which is similar to the idea of generalized 1-type Gauss maps. Based on this concept, the surfaces of revolution and the canal surfaces in the Euclidean three-space are classified. First of all, we show that the Gauss map of any surfaces of revolution with a unit speed profile curve is of generalized Cheng–Yau 1-type. At the same time, an oriented canal surface has a generalized Cheng–Yau 1-type Gauss map if, and only if, it is an open part of a surface of revolution or a torus.

Suggested Citation

  • Jinhua Qian & Xueshan Fu & Xueqian Tian & Young Ho Kim, 2020. "Surfaces of Revolution and Canal Surfaces with Generalized Cheng–Yau 1-Type Gauss Maps," Mathematics, MDPI, vol. 8(10), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1728-:d:425378
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