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J. Korean Math. Soc. 2005; 42(3): 447-455

Printed May 1, 2005

Copyright © The Korean Mathematical Society.

Surfaces of revolution with pointwise $1$-type Gauss map

Bang-Yen Chen, Miekyung Choi, and Young Ho Kim

Michigan State University, Kyungpook National University, Kyungpook National University

Abstract

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In this article, we introduce the notion of pointwise $1$-type Gauss map of the first and second kinds and study surfaces of revolution with such Gauss map. Our main results state that surfaces of revolution with pointwise $1$-type Gauss map of the first kind coincide with surfaces of revolution with constant mean curvature; and the right cones are the only rational surfaces of revolution with pointwise $1$-type Gauss map of the second kind.

Keywords: surfaces of revolution, circular cylinder, right cone, pointwise $1$-type Gauss map

MSC numbers: 53B25, 53C40

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