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A Differential Form Approach to Dirac Operators on Surfaces

  • Heikki OrelmaEmail author
  • Frank Sommen
Conference paper
  • 678 Downloads
Part of the Trends in Mathematics book series (TM)

Abstract

In this paper we study what is a suitable method to restrict the classical Dirac operator \(\partial _x\), defined on ℝm, to a k-surface \(S \subset \mathbb{R}^m\). The fundamental result is that for each k-surface S there exists (at least locally) a first order linear differential operator D k satisfying
$$d(dX^{k-1}f)|s = (-1)^{k-1}(dX^k\ D_k f)|s.$$
If \(S = \mathbb{R}^m\), then \(D_m = \partial _x\) is the classical Dirac operator.

Keywords

Dirac operator tangential Dirac operator restricted Dirac operator surface geometry surface monogenics 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of MathematicsTampere University of TechnologyTampereFinland
  2. 2.Department of Mathematical AnalysisGhent UniversityGentBelgium

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