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Type: Artigo de periódico
Title: Clifford And Extensor Calculus Anf The Riemann And Ricci Extensor Fields Of Deformed Structures (m, ∇′, η) And (m, ∇ G)
Author: Fernandez V.V.
Rodrifues Jr. W.A.
Moya A.M.
Da Rocha R.
Abstract: Here (the last paper in a series of four) we end our presentation of the basics of a systematical approach to the differential geometry of a smooth manifold M (supporting a metric field g and a general connection ∇) which uses the geometric algebras of multivector and extensors (fields) developed in previous papers. The theory of the Riemann and Ricci fields of a triple (M, ∇, g) is investigated for each particular open set U ⊂ M through the introduction of a geometric structure on U , i.e. a triple (U, γ, g), where γ is a general connection field on U and g is a metric extensor field associated to g. The relation between geometrical structures related to gauge extensor fields is clarified. These geometries may be said to be deformations one of each other. Moreover, we study the important case of a class of deformed Levi-Civita geometrical structures and prove key theorems about them that are important in the formulation of geometric theories of the gravitational field. © 2007 World Scientific Publishing Company.
Rights: fechado
Identifier DOI: 10.1142/S021988780700248X
Date Issue: 2007
Appears in Collections:Unicamp - Artigos e Outros Documentos

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