Almost complex structures on quaternion-Kähler manifolds and inner symmetric spaces
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- Gauduchon, P., Moroianu, A. & Semmelmann, U. Invent. math. (2011) 184: 389. doi:10.1007/s00222-010-0291-6
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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.