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Closed orientable surfaces and fold Gauss maps

Publicado en:Research In Mathematical Sciences. 11 (2): 37- - 2024-06-01 11(2), DOI: 10.1007/s40687-024-00451-0

Autores: de Jesus, C Mendes; Romero, Pantaleon D; Sanabria-Codesal, E

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Resumen

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 -> R 3 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f: M \rightarrow \mathbb {R}3$$\end{document} for which the Gauss map is a fold Gauss map.

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