Inventiones mathematicae

, Volume 184, Issue 2, pp 389–403

Almost complex structures on quaternion-Kähler manifolds and inner symmetric spaces

Article

DOI: 10.1007/s00222-010-0291-6

Cite this article as:
Gauduchon, P., Moroianu, A. & Semmelmann, U. Invent. math. (2011) 184: 389. doi:10.1007/s00222-010-0291-6

Abstract

We prove that compact quaternionic-Kähler manifolds of positive scalar curvature admit no almost complex structure, even in the weak sense, except for the complex Grassmannians Gr2(ℂn+2). We also prove that irreducible inner symmetric spaces M4n of compact type are not weakly complex, except for spheres and Hermitian symmetric spaces.

Mathematics Subject Classification (2000)

32Q60 57R20 53C26 53C35 53C15 

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Paul Gauduchon
    • 1
  • Andrei Moroianu
    • 1
  • Uwe Semmelmann
    • 2
  1. 1.CMLS, École PolytechniqueUMR 7640 du CNRSPalaiseauFrance
  2. 2.Mathematisches InstitutUniversität zu KölnKölnGermany