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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Teorema de holonomia normal

Aguirre, Sergio Julio Chion 30 August 2013 (has links)
Made available in DSpace on 2016-06-02T20:28:28Z (GMT). No. of bitstreams: 1 5611.pdf: 719770 bytes, checksum: 86c089b56af72cff83b5e7b8455ce765 (MD5) Previous issue date: 2013-08-30 / Financiadora de Estudos e Projetos / In this work we will introduce the concept of normal holonomy and restricted normal holonomy of a riemannian submanifold. They are subgroups of the orthogonal matrices that are realized from parallel translating normal vectors, along loops and null-homotopic loops respectively, using the normal connection. We will proof that the restricted normal holonomy is a Lie subgroup of the orthogonal matrices. With the aid of the Ambrose-Singer Theorem, which relates the concept of curvature with restricted normal holonomy, we will prove the Normal Holonomy Theorem which is the extrinsic analogue of the algebraic de Rham-Berger s Theorem. / Neste trabalho, vamos introduzir os conceitos de holonomia normal e holonomia normal restrita de uma subvariedade riemanniana, os quais são subgrupos das matrizes ortogonais que se realizam a partir de fazer translação paralela dos vetores normais, ao longo de lazos e lazos simplemente conexos respectivamente, usando a conexão normal. Vamos ver que a holonomia normal restrita é um subgrupo de Lie das matrizes ortogonais. Com o auxílio do Teorema de Ambrose-Singer, que relaciona o conceito de curvatura com holonomia normal restrita, vamos provar o Teorema Normal de Holonomia, análogo extrínseco do teorema de Rham-Berger algébrico.

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