Geometry of the parabolic subset of generically immersed 3-manifolds in R4

被引：0

作者：

Nabarro, A. C. ^{[1
]}

Fuster, M. C. Romero ^{[2
]}

Zanardo, M. C. ^{[1
]}

机构：

[1] Ave Trabalhador Sao Carlense,400 Ctr, BR-13566590 Sao Carlos, SP, Brazil

[2] Univ Valencia, Dept Matemat, Burjassot 46100, Valencia, Spain

来源：

RESEARCH IN THE MATHEMATICAL SCIENCES | 2024年 / 11卷 / 02期

基金：

巴西圣保罗研究基金会;

关键词：

Parabolic surface of 3-manifolds in R-4; Height functions; Geometrical characterizations for local singularities; CONTACT; SURFACES;

D O I：

10.1007/s40687-024-00450-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The parabolic subset of a 3-manifold generically immersed in R-4 is a surface. We analyze in this study the generic geometrical behavior of such surface, considered as a submanifold of R-4. Typical Singularity Theory techniques based on the analysis of the family of height functions are applied in order to describe the geometrical characterizations of different singularity types.

引用

页数：17

共 9 条

[1] Geometrical characterizations of singularities of the Gauss map on generically immersed 3-manifolds in R4
Nabarro, Ana Claudia
Romero-Fuster, Maria del Carmen
Zanardo, Maria Carolina
JOURNAL OF GEOMETRY, 2025, 116 (01)
[2] Generic Geometry of Stable Maps of 3-Manifolds into R4
Casonatto, C.
Fuster, M. C. Romero
Atique, R. Wik
BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2021, 52 (03): : 547 - 561
[3] Geometry of the parabolic subset of generically immersed 3-manifolds in R4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^4$$\end{document}
A. C. Nabarro
M. C. Romero Fuster
M. C. Zanardo
Research in the Mathematical Sciences, 2024, 11 (2)
[4] Self-conjugate vectors of immersed 3-manifolds in R6
Dreibelbis, Daniel
TOPOLOGY AND ITS APPLICATIONS, 2012, 159 (02) : 450 - 456
[5] Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds
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Mondino, Andrea
Schygulla, Johannes
MATHEMATISCHE ANNALEN, 2014, 359 (1-2) : 379 - 425
[6] Singular 3-manifolds in R5
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Soares Ruas, Maria Aparecida
Sacramento, Andrea de Jesus
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2022, 116 (01)
[7] ON 4-DIMENSIONAL 2-HANDLEBODIES AND 3-MANIFOLDS
Bobtcheva, Ivelina
Piergallini, Riccardo
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2012, 21 (12)
[8] The dual tree of a fold map germ from R3 to R4
Moya-Perez, J. A.
Nuno-Ballesteros, J. J.
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2023, 153 (03) : 958 - 977
[9] Complete 3-dimensional λ-translators in the Euclidean space R4
Li, Zhi
Wei, Guoxin
Chen, Gangyi
JOURNAL OF TOPOLOGY AND ANALYSIS, 2024, 16 (01) : 71 - 124

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