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Schur’s lemma for Kähler manifolds

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Abstract.

We give a necessary and sufficient condition for a Kähler manifold of complex dimension n ≧ 2 to be a complex space form in terms of its sectional curvatures, which is an extension of Schur’s lemma. Our study is related to a congruence theorem for circles in a complex space form

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Author notes

  1. Sadahiro Maeda

    Present address: Department of Mathematics, Saga University, 1 Honzyo, Saga, 840-8502, Japan

Authors and Affiliations

  1. Department of Mathematics, Nagoya Institute of Technology, Gokiso, Nagoya, 466-8555, Japan

    Toshiaki Adachi

  2. Department of Mathematics, Shimane University, Matsue, 690-8504, Japan

    Sadahiro Maeda

  3. Department of Mathematics, School of Medicine, Nihon University, Itabashi, Tokyo, 173-0032, Japan

    Seiichi Udagawa

Authors
  1. Toshiaki Adachi
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  2. Sadahiro Maeda
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  3. Seiichi Udagawa
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Corresponding author

Correspondence to Toshiaki Adachi.

Additional information

Dedicated to Professor Bang-Yen Chen on the occasion of his 65th birthday

The first author is partially supported by Grant-in-Aid for Scientific Research (C) (No. 17540072), Japan Society for the Promotion of Sciences.

Received: 6 October 2006

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Adachi, T., Maeda, S. & Udagawa, S. Schur’s lemma for Kähler manifolds. Arch. Math. 90, 163–172 (2008). https://doi.org/10.1007/s00013-007-2180-9

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  • DOI: https://doi.org/10.1007/s00013-007-2180-9

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