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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



$S^1$-quotients of quaternion-Kähler manifolds

Author: Fiammetta Battaglia
Journal: Proc. Amer. Math. Soc. 124 (1996), 2185-2192
MSC (1991): Primary 53C25; Secondary 58F05
MathSciNet review: 1307492
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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 $Sp(n)Sp(1)$. 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 $Gr_2(\mathbb {C} ^n)$.

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Fiammetta Battaglia
Affiliation: Dipartimento di Matematica Applicata G. Sansone via S. Marta 3 50139 Firenze Italy.

Keywords: Quaternion-K\"ahler manifolds, moment map, reduction
Received by editor(s): April 5, 1994
Received by editor(s) in revised form: December 16, 1994
Communicated by: Christopher Croke
Article copyright: © Copyright 1996 American Mathematical Society