A Characterization of Homogeneous Holomorphic Two-Spheres in Qn

Jie Fei, Jun Wang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

In this paper, we classify holomorphic curves in Qn with certain geometric conditions. We study the (1,0) part of kth covariant derivative about the second fundamental form denoted by a,k, 0≤k≤[n2]-2; the norm of its symmetric product is denoted by τk= | a,k· a,k|. It is proven that a holomorphic curve in Qn is homogeneous if the Gaussian curvature, the norm of the second fundamental form and τk are all constant. Moreover, all the homogeneous holomorphic curves are uniquely determined by our given examples, up to a rigid motion of Qn.

Original languageEnglish
Pages (from-to)35-66
Number of pages32
JournalJournal of Geometric Analysis
Volume31
Issue number1
DOIs
Publication statusPublished - Jan 2021

Keywords

  • Gaussian curvature
  • Holomorphic curves
  • Homogeneity
  • Hyperquadric
  • Rigidity
  • The second fundamental form

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