由圆片理的3中的最小和常数平均曲率曲面

IF 0.5 4区数学 Q3 MATHEMATICS

Bulletin of the Korean Mathematical Society Pub Date : 2019-01-01 DOI:10.4134/BKMS.B181266

Sung-Ho Park

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引用次数: 1

摘要

在S3中，我们对由圆片理的最小曲面和定常平均曲率曲面进行了分类。首先，我们证明了S3中由圆片理的最小表面要么是直纹的(即由测地线片理)，要么是旋转对称的(即在固定测地线的等距s1作用下不变)。其次，我们证明了，对于每个非负平均曲率，在S3中局部只有一个直纹cmc曲面达到等距。我们给出了S3中直纹cmc曲面的参数化(参见定理3)。

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MINIMAL AND CONSTANT MEAN CURVATURE SURFACES IN 3 FOLIATED BY CIRCLES

We classify minimal surfaces in S3 which are foliated by circles and ruled constant mean curvature (cmc) surfaces in S3. First we show that minimal surfaces in S3 which are foliated by circles are either ruled (that is, foliated by geodesics) or rotationally symmetric (that is, invariant under an isometric S1-action which fixes a geodesic). Secondly, we show that, locally, there is only one ruled cmc surface in S3 up to isometry for each nonnegative mean curvature. We give a parametrization of the ruled cmc surface in S3 (cf. Theorem 3).

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来源期刊

Bulletin of the Korean Mathematical Society 数学-数学

CiteScore

0.80

自引率

20.00%

发文量

审稿时长

6 months

期刊介绍： This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).