• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.315-330
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• 1998

Chen and Piccinni [7] have classified all compact surfaces in a Euclidean space $R^{2＋p}$ with 1-type generalized Gauss map. Being motivated by this result, the purpose of this paper is to consider the Lorentz version of the classification theorem and to obtain a complete classification of space-like surfaces in indefinite Euclidean space $R_{p}$ $^{2＋p}$ with 1-type generalized Gauss map.p.

• The Pure and Applied Mathematics
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• v.18 no.4
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• pp.369-377
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• 2011

In this article, we study generalized slant cylindrical surfaces (GSCS's) with pointwise 1-type Gauss map of the first and second kinds. Our main results state that GSCS's 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 polynomial kind GSCS's with pointwise 1-type Gauss map of the second kind.

• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.229-237
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• 2012

In this article, we study generalized slant cylindrical surfaces (GSCS's) with pointwise 1-type Gauss map of the first and second kinds. Our main results state that the right circular cones are the only rational kind GSCS's with pointwise 1-type Gauss map of the second kind.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1309-1330
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• 2016

As a generalizing certain geometric property occurred on the helicoid of 3-dimensional Euclidean space regarding the Gauss map, we study ruled submanifolds in a Euclidean space with pointwise 1-type Gauss map of the first kind. In this paper, as new examples of cylindrical ruled submanifolds in Euclidean space, we construct generalized circular cylinders and characterize such ruled submanifolds and minimal ruled submanifolds of Euclidean space with pointwise 1-type Gauss map of the first kind.