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

Jinhua Qian, Xueshan Fu, Xueqian Tian and Young Ho Kim
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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

Mathematics, 2020, vol. 8, issue 10, 1-12

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.

Keywords: surface of revolution; canal surface; Cheng–Yau operator; Gauss map (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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