旋转CMC曲面，椭圆曲线，weerstrass - \(\wp \)函数，代数

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2024-11-16 DOI:10.1007/s00013-024-02071-0

Rukmini Dey, Anantadulal Paul, Rahul Kumar Singh

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引用次数: 0

摘要

本文建立了\(\mathbb {E}_1^3\)中CMC旋转曲面族与某些特定椭圆曲线族之间的有趣联系。由于这种联系，我们证明了在\(\mathbb {E}_1^3\)的类空间CMC旋转曲面中，只有类空间柱体和标准双曲面是代数的。我们还证明了\(\mathbb E^3\)中CMC旋转曲面与椭圆曲线之间存在类似的联系。进一步，我们用它来重建\(\mathbb E^3\)中唯一的CMC代数旋转曲面是球体和右圆柱的事实。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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CMC surfaces of revolution, elliptic curves, Weierstrass-\(\wp \) functions, and algebraicity

This paper establishes an interesting connection between the family of CMC surfaces of revolution in \(\mathbb {E}_1^3\) and some specific families of elliptic curves. As a consequence of this connection, we show in the class of spacelike CMC surfaces of revolution in \(\mathbb {E}_1^3\), only spacelike cylinders and standard hyperboloids are algebraic. We also show that a similar connection exists between CMC surfaces of revolution in \(\mathbb E^3\) and elliptic curves. Further, we use this to reestablish the fact that the only CMC algebraic surfaces of revolution in \(\mathbb E^3\) are spheres and right circular cylinders.

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来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

期刊介绍： Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.