Differential Structure of the Hyperbolic Clifford Algebra

2014/03/13 by Notte-Cuello, Eduardo A., Rodrigues, Waldyr A.
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1403.3150

Abstract

This paper presents a thoughful review of: (a) the Clifford algebra Cl(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.

Related

• Duality Products of Multivectors and Multiforms, and Extensors
• The Hyperbolic Clifford Algebra of Multivecfors
• Covariant Derivatives of Mutivector and Extensor Fields
• Metric and Gauge Extensors
• Clifford algebra and the projective model of Hyperbolic spaces