Frontiers of Mathematics in China >

2019 , Vol. 14 >Issue 2: 315 - 348

DOI: 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
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  • School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received date: 25 Feb 2019

Accepted date: 22 Mar 2019

Published date: 15 Apr 2019

Copyright

2019 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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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.

Key words： Conformal minimal surface; isotropy order; constant curvature; linearly full

Cite this article

Xiaoxiang JIAO , Hong LI . Conformal minimal immersions with constant curvature from S2 to Q5[J]. Frontiers of Mathematics in China, 2019 , 14(2) : 315 -348 . DOI: 10.1007/s11464-019-0763-y

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