Subvariedades com curvatura de Moebius constante e fibrado normal plano

Antas, Mateus da Silva Rodrigues

doi:10.11606/T.55.2023.tde-28042023-182541

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Doctoral Thesis

DOI

https://doi.org/10.11606/T.55.2023.tde-28042023-182541

Document

Doctoral Thesis

Author

Antas, Mateus da Silva Rodrigues (Catálogo USP)

Full name

Mateus da Silva Rodrigues Antas

E-mail

Institute/School/College

Instituto de Ciências Matemáticas e de Computação

Knowledge Area

Mathematics

Date of Defense

2023-02-17

Published

São Carlos, 2023

Supervisor

Figueiredo Junior, Ruy Tojeiro de (Catálogo USP)

Committee

Figueiredo Junior, Ruy Tojeiro de (President)
Angulo, Martha Patrícia Dussan
Gomes, José Nazareno Vieira
Manfio, Fernando

Title in Portuguese

Subvariedades com curvatura de Moebius constante e fibrado normal plano

Keywords in Portuguese

forma de Moebius fechada, subvariedades com fibrado normal plano
Geometria de Moebius
métrica de Moebius
subvariedades com curvatura de Moebius constante
subvariedades conformemente Euclidianas.
subvariedades isoparamétricas de Moebius

Abstract in Portuguese

Nesta tese, classificamos as subvariedades f : Mn R n+p , n 5 e p = 2 ou n 6 e 2p n, que possuem curvatura de Moebius constante e fibrado normal plano. Também classificamos as subvariedades f : Mn R n+p , n3 p 1, conformemente Euclidianas e isoparamétricas de Moebius.

Title in English

Submanifolds with constant Moebius curvature and flat normal bundle

Keywords in English

closed Moebius form
conformally flat submanifolds.
Moebius geometry
Moebius metric
submanifolds with constant Moebius curvature, Moebius isoparametric submanifolds
submanifolds with flat normal bundle

Abstract in English

In this thesis, we classify submanifolds f : Mn R n+p , n 5 and p = 2 or n 6 and 2p n, with constant Moebius curvature and flat normal bundle. We also classify the class of conformally flat submanifolds f : Mn R n+p , n3 p 1, which are Moebius isoparametric.

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Publishing Date

2023-05-11

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