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The Weitzenböck machine

Published online by Cambridge University Press:  23 February 2010

Uwe Semmelmann
Affiliation:
Mathematisches Institut, Universität zu Köln, Weyertal 86-90, D-50931 Köln, Germany (email: uwe.semmelmann@math.uni-koeln.de)
Gregor Weingart
Affiliation:
Instituto de Matematicas (Unidad Cuernavaca), Universidad Nacional Autonoma de Mexico, Avenida Universidad s/n, Colonia Lomas de Chamilpa, 62210 Cuernavaca, Morelos, Mexico (email: gw@matcuer.unam.mx)
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Abstract

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Weitzenböck formulas are an important tool in relating local differential geometry to global topological properties by means of the so-called Bochner method. In this article we give a unified treatment of the construction of all possible Weitzenböck formulas for all irreducible, non-symmetric holonomy groups. We explicitly construct a basis of the space of Weitzenböck formulas. This classification allows us to find customized Weitzenböck formulas for applications such as eigenvalue estimates or Betti number estimates.

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2010

References

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