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Circle Actions and Morse Theory on Quaternion‐Kähler Manifolds
Author(s) -
Battaglia Fiammetta
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610798006930
Subject(s) - quaternion , mathematics , pure mathematics , action (physics) , isometric exercise , scalar curvature , hyperkähler manifold , manifold (fluid mechanics) , scalar (mathematics) , curvature , morse code , morse theory , mathematical analysis , sectional curvature , physics , geometry , computer science , quantum mechanics , medicine , mechanical engineering , telecommunications , engineering , physical therapy
In this paper we study quaternion‐Kähler manifolds endowed with an isometric S 1 ‐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 H P n .