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Geometric & Functional Analysis GAFA

, Volume 6, Issue 6, pp 899–942 | Cite as

Metrics with harmonic spinors

  • Christian Bär
Article

Abstract

We show that every closed spin manifold of dimensionn ≡ 3 mod 4 with a fixed spin structure can be given a Riemannian metric with harmonic spinors, i.e. the corresponding Dirac operator has a non-trivial kernel (Theorem A). To prove this we first compute the Dirac spectrum of the Berger spheresS n ,n odd (Theorem 3.1). The second main ingredient is Theorem B which states that the Dirac spectrum of a connected sumM1#M2 with certain metrics is close to the union of the spectra ofM1 and ofM2.

Keywords

Dirac Operator Spin Structure Main Ingredient Connected sumM1 Spin Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag 1996

Authors and Affiliations

  • Christian Bär
    • 1
  1. 1.Mathematisches InstitutUniversität FreiburgFreiburgGermany

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