$S^1$-quotients of quaternion-Kähler manifolds
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- by Fiammetta Battaglia PDF
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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 $Gr_2(\mathbb {C}^n)$.References
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Additional Information
- Fiammetta Battaglia
- Affiliation: Dipartimento di Matematica Applicata G. Sansone via S. Marta 3 50139 Firenze Italy.
- Email: fiamma@ingfi1.ing.unifi.it
- Received by editor(s): April 5, 1994
- Received by editor(s) in revised form: December 16, 1994
- Communicated by: Christopher Croke
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 2185-2192
- MSC (1991): Primary 53C25; Secondary 58F05
- DOI: https://doi.org/10.1090/S0002-9939-96-03208-X
- MathSciNet review: 1307492