Geometria diferencial de segunda ordem de variedades singulares em espaços euclidianos

Riul, Pedro Benedini

doi:10.11606/T.55.2019.tde-29092022-100901

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Doctoral Thesis

DOI

https://doi.org/10.11606/T.55.2019.tde-29092022-100901

Document

Doctoral Thesis

Author

Riul, Pedro Benedini (Catálogo USP)

Full name

Pedro Benedini Riul

E-mail

Institute/School/College

Instituto de Ciências Matemáticas e de Computação

Knowledge Area

Mathematics

Date of Defense

2019-02-18

Published

São Carlos, 2019

Supervisor

Ruas, Maria Aparecida Soares (Catálogo USP)
Sinha, Raúl Adrián Oset - (Co-supervisor) (Catálogo USP)

Committee

Ruas, Maria Aparecida Soares (President)
Fuster, Maria Del Carmen Romero
Garcia, Ronaldo Alves
Tari, Farid

Title in Portuguese

Geometria diferencial de segunda ordem de variedades singulares em espaços euclidianos

Keywords in Portuguese

Geometria diferencial
Segunda forma fundamental
Variedades singulares

Abstract in Portuguese

Esta tese é dedicada ao estudo da geometria de segunda ordem de variedades singulares de coposto 1 em espaços euclidianos, ou seja, ao estudo das propriedades geométricas relacionadas à segunda forma fundamental de tais variedades em pontos singulares. O foco será dado às superfícies de coposto 1 em R⁴ , no entanto também serão consideradas superfícies e 3-variedades de coposto 1 em R³ e R⁵ , respectivamente.

Title in English

Second order differential geometry of singular varieties in euclidean spaces

Keywords in English

Differential geometry
Second fundamental form
Singular varieties

Abstract in English

This thesis is dedicated to the study of the second order geometry of corank 1 singular varieties in euclidean spaces, that is, to the study of geometrical properties related to the second fundamental form of those varieties at singular points. The focus will be on corank 1 surfaces in R⁴ however corank 1 surfaces and 3-varieties in R³ and R⁵ , respectively, will also be conside.

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Publishing Date

2022-09-29

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