Closed orientable surfaces and fold Gauss maps

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-26 DOI:10.1007/s40687-024-00451-0

C. Mendes de Jesus, Pantaleón D. Romero, E. Sanabria-Codesal

引用次数: 0

Abstract

This paper describes how the elliptic and hyperbolic regions of a surface are related to stable Gauss maps on closed orientable surfaces immersed in three-dimensional space. We will show that for certain connected, closed, orientable surfaces containing a finite number of embedded circles that delineate two distinct types of regions, if all regions of one type are homeomorphic to a cylinder, then there exists an immersion \(f: M \rightarrow \mathbb {R}^3\) for which the Gauss map is a fold Gauss map.

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封闭可定向曲面和折叠高斯图

本文描述了曲面的椭圆区域和双曲区域如何与浸入三维空间的封闭可定向曲面上的稳定高斯映射相关。我们将证明，对于某些连通的、封闭的、可定向的曲面，其中包含有限数量的嵌入圆，这些嵌入圆划分了两种不同类型的区域，如果一种类型的所有区域都同构于圆柱体，那么存在一个浸入（f: M \rightarrow \mathbb {R}^3\），对于这个浸入，高斯图是一个折叠高斯图。

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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