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

• 成果类型: Article
• 署名作者: Gauduchon, Paul; Moroianu, Andrei; Semmelmann, Uwe
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; Ecole Polytechnique; University of Cologne
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-010-0291-6
• 发表日期: 2011
• 页码: 389-403
• 关键词: nonexistence

摘要

We prove that compact quaternionic-Kahler manifolds of positive scalar curvature admit no almost complex structure, even in the weak sense, except for the complex Grassmannians Gr(2)(a, (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.