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

Paul Gauduchon; Andrei Moroianu; Uwe Semmelmann

doi:10.1007/s00222-010-0291-6

paper

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

arXiv:1003.5172 · 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 $G r_{2} (C^{n + 2})$ . We also prove that irreducible inner symmetric spaces $M^{4 n}$ of compact type are not weakly complex, except for spheres and Hermitian symmetric spaces.

the related manuscript arXiv:1006.2457 was merged into this new version