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Differential Structure of the Hyperbolic Clifford Algebra

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Abstract

This paper presents a thoughful review of: (a) the Clifford algebra \({\mathcal{C}{\ell} (H_V)}\) of multivecfors which is naturally associated with a hyperbolic space H V ; (b) the study of the properties of the duality product of multivectors and multiforms; (c) the theory of k multivector and l multiform variables multivector extensors over V and (d) the use of the above mentioned structures to present a theory of the parallelism structure on an arbitrary smooth manifold introducing the concepts of covariant derivarives, deformed covariant derivatives and relative covariant derivatives of multivector, multiform fields and extensors fields.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de La Serena, Av. Cisternas, 1200, La Serena, Chile

    Eduardo A. Notte-Cuello

  2. Institute of Mathematics, Statistics and Scientific Computation, IMECC-UNICAMP, CP 6065, 13083-859, Campinas, SP, Brazil

    Waldyr A. Rodrigues Jr.

Authors
  1. Eduardo A. Notte-Cuello
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  2. Waldyr A. Rodrigues Jr.
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Correspondence to Eduardo A. Notte-Cuello.

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Notte-Cuello, E.A., Rodrigues, W.A. Differential Structure of the Hyperbolic Clifford Algebra. Adv. Appl. Clifford Algebras 25, 169–218 (2015). https://doi.org/10.1007/s00006-014-0482-0

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