Closed orientable surfaces and fold Gauss maps-Reference-Cited by-同舟云学术

Closed orientable surfaces and fold Gauss maps

Published:2024-04-26 Issue:2 Volume:11 Page:
ISSN:2522-0144
Container-title:Research in the Mathematical Sciences
language:en
Short-container-title:Res Math Sci

Author:

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

Abstract

AbstractThis 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

$$f: M \rightarrow \mathbb {R}^3$$

f : M → R 3 for which the Gauss map is a fold Gauss map.

Funder

INDI23/17

Fapemig / INCTMat

Universitat Politècnica de València

Publisher

Springer Science and Business Media LLC

Link

https://link.springer.com/content/pdf/10.1007/s40687-024-00451-0.pdf

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