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On positive quaternionic Kähler manifolds with certain symmetry rank

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Abstract

Let M be a positive quaternionic Kähler 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 Kähler manifolds equipped with symmetry. The main idea is to use the connectedness theorem for quaternionic Kähler manifolds with a group action and the induction arguments on the dimension of the manifold.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Kusong-dong, Yusong-gu, Daejon, 305-701, Korea

    Jin Hong Kim

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  1. Jin Hong Kim
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Correspondence to Jin Hong Kim.

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Kim, J.H. On positive quaternionic Kähler manifolds with certain symmetry rank. Isr. J. Math. 172, 157–169 (2009). https://doi.org/10.1007/s11856-009-0069-y

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  • DOI: https://doi.org/10.1007/s11856-009-0069-y

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