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arXiv · 1003.5172

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

Paul Gauduchon·Andrei Moroianu·Uwe Semmelmann
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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 $Gr_2(C^{n+2})$. 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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Paul Gauduchon, Andrei Moroianu, Uwe Semmelmann. 2011-04-23. Almost complex structures on quaternion-Kähler manifolds and inner symmetric spaces. https://doi.org/10.1007/s00222-010-0291-6

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