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arXiv · 1911.05383

Rigidity of conformal minimal immersions of constant curvature from $S^2$ to $Q_4$

Xiaoxiang Jiao·Mingyan Li·Hong Li
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Abstract

Geometry of conformal minimal two-spheres immersed in $G(2,6;\mathbb{R})$ is studied in this paper by harmonic maps. We construct a non-homogeneous constant curved minimal two-sphere in $G(2,6;\mathbb{R})$, and give a classification theorem of linearly full conformal minimal immersions of constant curvature from $S^2$ to $G(2,6;\mathbb{R})$, or equivalently, a complex hyperquadric $Q_{4}$, which illustrates minimal two-spheres of constant curvature in $Q_{4}$ are in general not congruent.

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Xiaoxiang Jiao, Mingyan Li, Hong Li. 2019-11-13. Rigidity of conformal minimal immersions of constant curvature from $S^2$ to $Q_4$. https://arxiv.org/abs/1911.05383

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