Partial Classification Results for Positive Quaternion Kaehler Manifolds

2009/11/24 by Manuel Amann, Amann, Manuel
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.0911.4587

arxiv created 2009/11/24 · arxiv updated 2009/12/08

Abstract

Positive Quaternion Kaehler Manifolds are Riemannian manifolds with holonomy contained in Sp(n)Sp(1) and with positive scalar curvature. Conjecturally, they are symmetric spaces. We prove this conjecture in dimension 20 under additional assumptions and we provide recognition theorems for quaternionic projective spaces (in low dimensions) as well as the real Grassmanian (which is Positive Quaternion Kaehler).

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