Geometric & Functional Analysis GAFA

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

Metrics with harmonic spinors

  • Christian Bär


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.


Dirac Operator Spin Structure Main Ingredient Connected sumM1 Spin Manifold 
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Copyright information

© Birkhäuser Verlag 1996

Authors and Affiliations

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

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