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.
Circle actions and Morse theory on quaternion-Kaehler manifolds / F. BATTAGLIA. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - STAMPA. - 59:(1999), pp. 345-358.
Circle actions and Morse theory on quaternion-Kaehler manifolds
BATTAGLIA, FIAMMETTA
1999
Abstract
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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