On positive quaternionic Kahler manifolds with certain symmetry rank

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Let M be a positive quaternionic Kahler manifold of real dimension 4m. In this paper we show that if the symmetry rank of M is greater than or equal to [m/2] + 3, then M is isometric to HP (m) or Gr2(C (m+2)). This is sharp and optimal, and will complete the classification result of positive quaternionic Kahler manifolds equipped with symmetry. The main idea is to use the connectedness theorem for quaternionic Kahler manifolds with a group action and the induction arguments on the dimension of the manifold.
Publisher
HEBREW UNIV MAGNES PRESS
Issue Date
2009-07
Language
English
Article Type
Article
Keywords

CURVED MANIFOLDS; CURVATURE; CLASSIFICATION

Citation

ISRAEL JOURNAL OF MATHEMATICS, v.172, no.1, pp.157 - 169

ISSN
0021-2172
DOI
10.1007/s11856-009-0069-y
URI
http://hdl.handle.net/10203/96546
Appears in Collection
MA-Journal Papers(저널논문)
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