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Minimal two-spheres with constant curvature in the quaternionic projective space

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Abstract

In this paper we completely classify the homogeneous two-spheres, especially, the minimal homogeneous ones in the quaternionic projective space ℍℙn. According to our classification, more minimal constant curved two-spheres in ℍℙn are obtained than what Ohnita conjectured in the paper Homogeneous harmonic maps into complex projective spaces. Tokyo J Math, 1990, 13: 87–116".

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11471299, 11401481 and 11331002). The authors express gratitude to the referees for the helpful comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Xi’an Jiaotong-Liverpool University, Suzhou, 215123, China

    Jie Fei

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Chiakuei Peng

  3. Department of Mathematics, University of Science and Technology of China, Hefei, 230026, China

    Xiaowei Xu

  4. Wu Wen-Tsun Key Laboratory of Mathematics, University of Science and Technology of China Chinese Academy of Sciences, Hefei, 230026, China

    Xiaowei Xu

Authors
  1. Jie Fei
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  2. Chiakuei Peng
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  3. Xiaowei Xu
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Correspondence to Xiaowei Xu.

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Fei, J., Peng, C. & Xu, X. Minimal two-spheres with constant curvature in the quaternionic projective space. Sci. China Math. 63, 993–1006 (2020). https://doi.org/10.1007/s11425-018-9348-y

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  • DOI: https://doi.org/10.1007/s11425-018-9348-y

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