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Clifford analysis on the hyperbolic unit ball

David Eelbode (UGent)
(2004)
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(UGent)
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Abstract
In this thesis we consider a projective model for the hyperbolic unit ball, realized as the manifold of rays inside the future cone in the real orthogonal space R1,m, i.e. the flat Minkowksi space-time. Using Clifford algebras it is possible to define a Clifford algebra structure on this manifold, and this structure enables us to define the Dirac operator on the hyperbolic unit ball as the Dirac operator on flat Minkowski space-time acting on the sections of a homogeneous Clifford line bundle, which is an associated principal fibre bundle. This thesis then deals with a function theory for Clifford algebra valued nullsolutions for the Dirac operator on the hyperbolic unit ball, the so-called hyperbolic monogenics.
Keywords
hyperbolic unit ball, Clifford analysis, Minkowski space, Dirac operator

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Citation

Please use this url to cite or link to this publication:

Chicago
Eelbode, David. 2004. “Clifford Analysis on the Hyperbolic Unit Ball”. Ghent, Belgium.
APA
Eelbode, D. (2004). Clifford analysis on the hyperbolic unit ball. Ghent, Belgium.
Vancouver
1.
Eelbode D. Clifford analysis on the hyperbolic unit ball. [Ghent, Belgium]; 2004.
MLA
Eelbode, David. “Clifford Analysis on the Hyperbolic Unit Ball.” 2004 : n. pag. Print.
@phdthesis{4108131,
  abstract     = {In this thesis we consider a projective model for the hyperbolic unit ball, realized as the manifold of rays inside the future cone in the real orthogonal space R1,m, i.e. the flat Minkowksi space-time. Using Clifford algebras it is possible to define a Clifford algebra structure on this manifold, and this structure enables us to define the Dirac operator on the hyperbolic unit ball as the Dirac operator on flat Minkowski space-time acting on the sections of a homogeneous Clifford line bundle, which is an associated principal fibre bundle. This thesis then deals with a function theory for Clifford algebra valued nullsolutions for the Dirac operator on the hyperbolic unit ball, the so-called hyperbolic monogenics.},
  author       = {Eelbode, David},
  language     = {eng},
  pages        = {267},
  school       = {Ghent University},
  title        = {Clifford analysis on the hyperbolic unit ball},
  year         = {2004},
}