Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 53C25, 58F05

Retrieve articles in all journals with MSC (1991): 53C25, 58F05


Additional Information

Fiammetta Battaglia
Affiliation: Dipartimento di Matematica Applicata G. Sansone\ via S. Marta 3\ 50139 Firenze\ Italy.
Email: fiamma@ingfi1.ing.unifi.it

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03208-X
PII: S 0002-9939(96)03208-X
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