rp - 3中克莱因瓶的不可嵌入性与劳森猜想

Q2 Arts and Humanities

Revista de la Academia Colombiana de Ciencias Exactas, Fisicas y Naturales Pub Date : 2023-10-17 DOI:10.18257/raccefyn.29(110).2005.2151

Oscar Perdomo

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引用次数: 0

摘要

1985年Montiel &Ros证明了S3中唯一的最小环面是Clifford环面，其拉普拉斯的第一个特征值为2。在这里，我们将首先证明在RP3中不存在嵌入克莱因瓶。事实上，我们将证明RP3中唯一可嵌入的非定向封闭曲面是那些具有奇欧拉特征的曲面。稍后，我们将给出Montiel &Ros的结果，假设最小环面具有{x， -x}对称性。

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NONEMBEDDABILITY OF THE KLEIN BOTTLE IN RP 3 AND LAWSON’S CONJECTURE

In 1985 Montiel & Ros showed that the only minimal torus in S3 , for which the first eigenvalue of the Laplacian is 2, is the Clifford torus. Here, we will show first the nonexistence of an embedded Klein bottle in RP3 . Indeed we will prove that the only non orientable closed surfaces that can be embedded in RP3 are those with odd Euler characteristic. Later on, we will give another proof of Montiel & Ros’ result, assuming that the minimal torus has {x, –x} simmetry.

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来源期刊

Revista de la Academia Colombiana de Ciencias Exactas, Fisicas y Naturales Arts and Humanities-History and Philosophy of Science

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

28 weeks