Circle Actions and Morse Theory on Quaternion‐Kähler Manifolds | Zendy

Battaglia Fiammetta | Zendy

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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 .

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