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Journal of University of Chinese Academy of Sciences ›› 2021, Vol. 38 ›› Issue (6): 729-734.DOI: 10.7523/j.issn.2095-6134.2021.06.002

• Innovation Article • Previous Articles     Next Articles

Construction of totally real surfaces in complex Grassmannians

JIAO Xiaoxiang, XIN Jialin   

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2019-11-20 Revised:2020-02-04 Online:2021-11-15
  • Supported by:
    Supported by the National Natural Science Foundation of China (11871450)

Abstract: We present a construction of the complex Grassmannian G(2,n+2) as a quotient of some minimal submanifold Qn+1 of $\mathbb{H}$Pn+1, then show that a surface in G(2,n+2) can be horizontally lifted to Qn+1 if and only if it is totally real.

Key words: Grassmannian, totally real surface, horizontal lift

CLC Number: