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Annals of Global Analysis and Geometry

, Volume 37, Issue 2, pp 163–171 | Cite as

Generic metrics and the mass endomorphism on spin three-manifolds

  • Andreas HermannEmail author
Article

Abstract

Let (M, g) be a closed Riemannian spin manifold. The constant term in the expansion of the Green function for the Dirac operator at a fixed point \({p\in M}\) is called the mass endomorphism in p associated to the metric g due to an analogy to the mass in the Yamabe problem. We show that the mass endomorphism of a generic metric on a three-dimensional spin manifold is nonzero. This implies a strict inequality which can be used to avoid bubbling-off phenomena in conformal spin geometry.

Keywords

Conformal differential geometry Spin geometry 

Mathematics Subject Classification (2000)

53A30 53C27 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.NWF I - MathematikUniversität RegensburgRegensburgGermany

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