Cohomology Groups of Harmonic Spinors on Conformally Flat Manifolds

  • Tosiaki Kori
Part of the Trends in Mathematics book series (TM)


We shall investigate various properties of the sheaf of harmonic spinors N on C2 and, more generally, on conformally flat spin 4-manifolds. We prove the Runge approximation theorem on C2, and the vanishing of cohomologies; H 1 (C 2,N) = 0 and H 1(S 4, N) = 0. We shall introduce a concept of divisors of meromorphic spinors on a compact conformally flat spin 4-manifold, and give an analogy of Riemann-Roch theorem.


Harmonic spinors conformally flat manifold Runge theorem Riemann-Roch theorem 

Mathematics Subject Classification (2000)

Primary 58G30 Secondary 53C21 


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Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • Tosiaki Kori
    • 1
  1. 1.Department of Mathematics School of Science and EngineeringWaseda UniversityTokyoJapan

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