Geometric & Functional Analysis GAFA

, Volume 5, Issue 3, pp 604–618 | Cite as

Complex contact structures and the first eigenvalue of the dirac operator on Kähler manifolds

  • K. -D. Kirchberg
  • U. Semmelmann


In this paper Kählerian Killing spinors on manifolds of complex dimensionm=4l+3 are constructed. The construction is based on a theorem which states that a closed Kähler Einstein manifold of complex dimension 4l+3 and positive scalar curvature admits a Kählerian Killing spinor if and only if there is a complex (2l+1)-contact structure. In particular, any complex contact structure in the usual sense gives rise to such a generalized contact structure. Using this, new examples of Kählerian Killing spinors are obtained.


Scalar Curvature Dirac Operator Contact Structure Complex Dimension Usual Sense 
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Copyright information

© Birkhäuser Verlag 1995

Authors and Affiliations

  • K. -D. Kirchberg
    • 1
  • U. Semmelmann
    • 2
  1. 1.Institut für Reine Mathematik (SFB 288)Humboldt-Universität zu BerlinBerlinGermany
  2. 2.Mathematisches InstitutUniversität BonnBonnGermany

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