Conformal minimal immersions with constant curvature from S2 to Q5

doi:10.1007/s11464-019-0763-y

Front. Math. China

2019, Vol. 14

Issue (2) : 315-348 https://doi.org/10.1007/s11464-019-0763-y

RESEARCH ARTICLE

Conformal minimal immersions with constant curvature from S² to Q₅

Xiaoxiang JIAO, Hong LI(

)

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

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Abstract

We study the geometry of conformal minimal two spheres immersed in G(2; 7; $ℝ$ ): Then we classify the linearly full irreducible conformal minimal immersions with constant curvature from S² to G(2; 7; $ℝ$ ); or equivalently, a complex hyperquadric Q5 under some conditions. We also completely determine the Gaussian curvature of all linearly full totally unramified irreducible and all linearly full reducible conformal minimal immersions from S² to G(2; 7; $ℝ$ ) with constant curvature. For reducible case, we give some examples, up to SO(7) equivalence, in which none of the spheres are congruent, with the same Gaussian curvature.

Keywords Conformal minimal surface isotropy order constant curvature linearly full

Corresponding Author(s): Hong LI

Issue Date: 14 May 2019

Cite this article:

Xiaoxiang JIAO,Hong LI. Conformal minimal immersions with constant curvature from S² to Q₅[J]. Front. Math. China, 2019, 14(2): 315-348.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-019-0763-y
https://academic.hep.com.cn/fmc/EN/Y2019/V14/I2/315

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