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On spacelike rotational surfaces with pointwise 1-type Gauss map

Ugur Dursun
대한수학회 (The Korean Mathematical Society)|2015.01|대한수학회보 (Bulletin of the KMS)|제52권 제1호|pp. 301-312

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참고문헌

키워드

parallel mean curvature vectorpointwise 1-type Gauss maprotational surfacesnormal bundle
주제분류수학

초록

In this paper, we study a class of spacelike rotational surfaces in the Minkowski 4-space $\mathbb E^4_1$ with meridian curves lying in 2-dimensional spacelike planes and having pointwise 1-type Gauss map. We obtain all such surfaces with pointwise 1-type Gauss map of the first kind. Then we prove that the spacelike rotational surface with flat normal bundle and pointwise 1-type Gauss map of the second kind is an open part of a spacelike 2-plane in $\mathbb E^4_1$.

Abstract

In this paper, we study a class of spacelike rotational surfaces in the Minkowski 4-space $\mathbb E^4_1$ with meridian curves lying in 2-dimensional spacelike planes and having pointwise 1-type Gauss map. We obtain all such surfaces with pointwise 1-type Gauss map of the first kind. Then we prove that the spacelike rotational surface with flat normal bundle and pointwise 1-type Gauss map of the second kind is an open part of a spacelike 2-plane in $\mathbb E^4_1$.

참고문헌 (21)

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