𝑆¹-quotients of quaternion-Kähler manifolds

Abstract

The notion of symplectic reduction has been generalized to manifolds endowed with other structures, in particular to quaternion-Kähler manifolds, namely Riemannian manifolds with holonomy in S p ( n ) S p ( 1 ) Sp(n)Sp(1) . In this work we prove that the only complete quaternion-Kähler manifold with positive scalar curvature obtainable as a quaternion-Kähler quotient by a circle action is the complex Grassmannian G r 2 ( C n ) Gr_2(\mathbb {C}^n) .