C. Mendes de Jesus, Pantaleón D. Romero, E. Sanabria-Codesal
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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.
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。
期刊介绍：
Research in the Mathematical Sciences is an international, peer-reviewed hybrid journal covering the full scope of Theoretical Mathematics, Applied Mathematics, and Theoretical Computer Science. The Mission of the Journal is to publish high-quality original articles that make a significant contribution to the research areas of both theoretical and applied mathematics and theoretical computer science.
This journal is an efficient enterprise where the editors play a central role in soliciting the best research papers, and where editorial decisions are reached in a timely fashion. Research in the Mathematical Sciences does not have a length restriction and encourages the submission of longer articles in which more complex and detailed analysis and proofing of theorems is required. It also publishes shorter research communications (Letters) covering nascent research in some of the hottest areas of mathematical research. This journal will publish the highest quality papers in all of the traditional areas of applied and theoretical areas of mathematics and computer science, and it will actively seek to publish seminal papers in the most emerging and interdisciplinary areas in all of the mathematical sciences. Research in the Mathematical Sciences wishes to lead the way by promoting the highest quality research of this type.
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