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Master's Dissertation
DOI
10.11606/D.55.2018.tde-24082018-105842
Document
Author
Full name
Antonio Carlos Nogueira
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1993
Supervisor
Committee
Ruas, Maria Aparecida Soares (President)
Asperti, Antonio Carlos
Baldin, Yuriko Yamamoto
Title in Portuguese
IMERSÔES JUSTAS DE VARIEDADES EM ESPAÇOS EUCLIDEANOS
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Uma aplicação f: M → Em, de um espaço topológico compacto e conexo em um espaço Euclideano é justa se para todo semi-espaço fechado h ⊂ Em, a inclusão f-1(h) → M induz um monomorfismo em Z2-homologia de Cech. Neste trabalho consideramos aplicações com esta propriedade, enfatizando o estudo de propriedades de imersões justas de variedades em espaços euclideanos. Para variedades de dimensão 2 justeza é equivalente a curvatura total absoluta sendo mínima. Nosso principal objetivo é discutir a existência de imersões justas para superfícies em E3. Segue do trabalho de N. Kuiper, e de um resultado recente de F. Haab, que todas as superfícies, exceto o plano projetivo (x = 1), a garrafa de Klein (x = O) e o plano projetivo com uma alça (x = -1), admitem imersão justa em E3. Estudamos também uma família genérica especial de aplicações justas C-estáveis do plano projetivo em E3.
Title in English
Tight embeddings in Euclidean and hyperbolic spaces
Keywords in English
Not available
Abstract in English
A mapping f : M → Em, from a topological compact, connected space into Euclidean space is tight if for every closed semi-space h ⊂ Em, the inclusion f-1 (h) → M induces a monomorphism in Cech Z2-homology. In this work we consider mappings with this property, emphasizing the study of properties of tight immersions of manifolds into Euclidean space. For 2-manifolds tightness is equivalent to the total absolute curvature being minimal. Our main purpose is to discuss the existence of tight immersions for surfaces into E3. It follows from the work of N. Kuiper, and recent result of F. Haab that all surfaces admit a tight immersion, except the projective plane (x = 1), the Klein's bottle (x = 0) and the projective plane with one handle (x = -1). We also study a special generic family of C-tight mapping from the projective plane into E3.
 
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Publishing Date
2018-08-24
 
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