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

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

2010-03-26

arxiv.org/abs/1003.5172v3

Inventiones Mathematicae vol. 184 no. 2, 389-403 (2011)

Mathematics

Differential Geometry

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

Scientific paper

10.1007/s00222-010-0291-6

We prove that compact quaternionic-K\"ahler manifolds of positive scalar
curvature admit no almost complex structure, even in the weak sense, except for
the complex Grassmannians $Gr_2(C^{n+2})$. We also prove that irreducible inner
symmetric spaces $M^{4n}$ of compact type are not weakly complex, except for
spheres and Hermitian symmetric spaces.

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