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CIRCLE ACTIONS AND MORSE THEORY ON QUATERNION-KÄHLER MANIFOLDS

Published online by Cambridge University Press:  01 February 1999

FIAMMETTA BATTAGLIA
FIAMMETTA BATTAGLIA
Affiliation:
Dipartimento di Matematica, Applicata G. Sansone, via S. Marta 3, 50139 Firenze, Italy. E-mail: [email protected]
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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.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 59 , Issue 1 , February 1999 , pp. 345 - 358
Copyright
The London Mathematical Society 1999

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