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Journal of the London Mathematical Society 1999 59(1):345-358; doi:10.1112/S0024610798006930
© 1999 by London Mathematical Society
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© The London Mathematical Society

Circle Actions and Morse Theory on Quaternion-Kähler Manifolds

Fiammetta Battaglia

Dipartimento di Matematica, Applicata G. Sansone via S. Marta 3, 50139 Firenze, Italy. E-mail: fiamma{at}dma.unifi.it

Received 29 August 1996. Revision received 26 February 1997.

In this paper we study quaternion-Kähler manifolds endowed with an isometric S1-action. We consider the corresponding moment map µ and prove that the only compact quaternion-Kähler manifold with positive scalar curvature which admits an isometric circle action free on µ–1(0) is the quaternionic projective space HPn.


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