ON POSITIVE QUATERNIONIC KAHLER MANIFOLDS WITH b(4)=1

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Let M be a positive quaternionic kahler manifold of dimension 4m. In earlier papers, Fang and the first author showed that if the symmetry rank is greater than or equal to [m/2]+ 3, then M is isometric to HPm or Gr(2)(Cm+2). The goal of this paper is to give a more refined classification result for positive quaternionic Kahler manifolds (in particular, of relatively low dimension or with even m) whose fourth Betti number equals one. To be precise, we show in this paper that if the symmetry rank of M with b(4)(M) = 1 is no less than [m/2] + 2 for in >= 5, then M is isometric to HPm.
Publisher
OSAKA JOURNAL OF MATHEMATICS
Issue Date
2012-09
Language
English
Article Type
Article
Keywords

SYMMETRY-RANK; CURVATURE; CLASSIFICATION

Citation

OSAKA JOURNAL OF MATHEMATICS, v.49, no.3, pp.551 - 562

ISSN
0030-6126
URI
http://hdl.handle.net/10203/102272
Appears in Collection
MA-Journal Papers(저널논문)
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