The notion of symplectic reduction has been generalized to manifolds endowed with other structures, in particular to quaternion-K ̈hler manifolds, namely Riemannian manifolds with holonomy in Sp(n)Sp(1). In this work we prove that the only complete quaternion-K ̈hler manifold with positive scalar curvature obtainable as a quaternion-K ̈hler quotient by a circle action is the complex Grassmannian Gr2 (Cn ).
S^1-QUOTIENTS OF QUATERNION-KAEHLER MANIFOLDS / F. BATTAGLIA. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 124:(1996), pp. 2185-2191.
S^1-QUOTIENTS OF QUATERNION-KAEHLER MANIFOLDS
BATTAGLIA, FIAMMETTA
1996
Abstract
The notion of symplectic reduction has been generalized to manifolds endowed with other structures, in particular to quaternion-K ̈hler manifolds, namely Riemannian manifolds with holonomy in Sp(n)Sp(1). In this work we prove that the only complete quaternion-K ̈hler manifold with positive scalar curvature obtainable as a quaternion-K ̈hler quotient by a circle action is the complex Grassmannian Gr2 (Cn ).
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