• JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
 
  Bookmark and Share
 
 
Doctoral Thesis
DOI
10.11606/T.45.2007.tde-22062007-170014
Document
Author
Full name
Leandro Gustavo Gomes
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2007
Supervisor
Committee
Forger, Frank Michael (President)
Bursztyn, Henrique
Kochloukov, Plamen Emilov
Negreiros, Caio Jose Colletti
Piccione, Paolo
Title in Portuguese
Estruturas polissimpléticas e multissimpléticas em variedades e fibrados
Keywords in Portuguese
Formas Multissimpléticas
Polissimpléticas
Teorema de Darboux
Abstract in Portuguese
Neste trabalho, introduzimos uma nova classe de formas multilineares alternadas e de formas diferenciais, chamadas de formas polilagrangeanas (no caso de formas a valores vetoriais) ou multilagrangeanas (no caso de formas parcialmente horizontais em relação a um subespaço ou subfibrado dado), que são caracterizadas pela existência de um tipo especial de subespaço ou subfibrado maximal isotrópico chamado, respectivamente, de polilagrangeano ou multilagrangeano. Revela-se que estas constituem o arcabouço adequado para a formulação de um teorema de Darboux em nível algébrico. Combinando esta nova estrutura algébrica com propriedades padrão de integrabilidade (d! = 0) nos permite deduzir o teorema de Darboux no contexto geométrico (existência de coordenadas locais canônicas). Estruturas polissimpléticas e multissimpléticas, inclusive todas aquelas que aparecem no formalismo hamiltoniano covariante da teoria clássica dos campos, são contidas como caso especial.
Title in English
Polysymplectic and Multisymplectic forms on Manifolds and Fiber Bundles
Keywords in English
Darboux theorem
polysymplectic and multisymplectic forms
Abstract in English
In this thesis, we introduce a new class of multilinear alternating forms and of differential forms called polylagrangean (in the case of vector-valued forms) or multilagrangean (in the csae of forms that are partially horizontal with respect to a given subspace or subbundle), characterized by the existence of a special type of maximal isotropic subspace or subbundle called polylagrangean or multilagrangean, respectively. As it turns out, these constitute the adequate framework for the formulation of an algebraic Darboux theorem. Combining this new algebraic structure with standard integrability conditions (d! = 0) allows us to derive a geometric Darboux theorem (existence of canonical local coordinates). Polysymplectic and multisymplectic structures, including all those that appear in the covariant hamiltonian formalism of classical field theory, are contained as a special case.
 
WARNING - Viewing this document is conditioned on your acceptance of the following terms of use:
This document is only for private use for research and teaching activities. Reproduction for commercial use is forbidden. This rights cover the whole data about this document as well as its contents. Any uses or copies of this document in whole or in part must include the author's name.
tese.pdf (435.93 Kbytes)
Publishing Date
2007-06-25
 
WARNING: Learn what derived works are clicking here.
All rights of the thesis/dissertation are from the authors
Centro de Informática de São Carlos
Digital Library of Theses and Dissertations of USP. Copyright © 2001-2019. All rights reserved.