FANO MANIFOLDS, CONTACT STRUCTURES, AND QUATERNIONIC GEOMETRY

1995/06/01 by Claude LeBrun · 4 citations
Mathematics · Physics and Astronomy · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Mathematics #Scalar curvature #Holomorphic function #Twistor space #Twistor theory #Pure mathematics #Kähler manifold #Codimension #Manifold (fluid mechanics) #Mathematical analysis #Integrable system #Curvature #Geometry

paper · doi:10.1142/s0129167x95000146

openalex publication_date 1995/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21

Abstract

Let Z be a compact complex (2n+1)-manifold which carries a complex contact structure, meaning a codimension-1 holomorphic sub-bundle D⊂TZ which is maximally non-integrable. If Z admits a Kähler-Einstein metric of positive scalar curvature, we show that it is the Salamon twistor space of a quaternion-Kähler manifold (M 4n , g). If Z also admits a second complex contact structure [Formula: see text], then Z=CP 2n+1 . As an application, we give several new characterizations of the Riemannian manifold HP n = Sp(n+1)/(Sp(n)×Sp(1)).

Citations

• A Finiteness Theorem for Quaternionic-Kaehler Manifolds with Positive Scalar Curvature

Cited by

• Hypermultiplet metric and D-instantons
• Darboux Charts Around Holomorphic Legendrian Curves and Applications
• M-theory on `toric'G2cones and its type II reduction
• Quaternion-Kähler manifold [wikipedia]