具有广义1型高斯映射的运河表面

IF 0.6 4区数学 Q3 MATHEMATICS

Revista De La Union Matematica Argentina Pub Date : 2021-05-31 DOI:10.33044/REVUMA.1685

J. Qian, Mengfei Su, Young Ho Kim

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引用次数: 5

摘要

本文考虑了一种基于欧几里得三维空间中运河表面高斯图G的分类方法。对于满足∆G = fG+gC的子流形，我们引入广义1型高斯映射的概念，其中∆为拉普拉斯算子，C为常数向量，(f, G)为非零光滑函数。首先，我们证明了欧几里得三维空间中任意具有单位速度轮廓曲线的旋转曲面的高斯映射是广义1型的。同时，讨论了具有广义1型高斯映射的运河表面。

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Canal surfaces with generalized 1-type Gauss map

This work considers a kind of classification of canal surfaces in terms of their Gauss map G in Euclidean 3-space. We introduce the notion of generalized 1-type Gauss map for a submanifold that satisfies ∆G = fG+gC, where ∆ is the Laplace operator, C is a constant vector, and (f, g) are non-zero smooth functions. First of all, we show that the Gauss map of any surface of revolution with unit speed profile curve in Euclidean 3-space is of generalized 1-type. At the same time, the canal surfaces with generalized 1-type Gauss map are discussed.

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来源期刊

Revista De La Union Matematica Argentina MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Revista de la Unión Matemática Argentina is an open access journal, free of charge for both authors and readers. We publish original research articles in all areas of pure and applied mathematics.