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Li, Mingyan; Jiao, Xiaoxiang; He, Ling

Classification of conformal minimal immersions of constant curvature from \(S^2\) to \(Q_3\). (English) Zbl 1357.53069

J. Math. Soc. Japan 68, No. 2, 863-883 (2016).
Summary: In this paper, we study geometry of conformal minimal two-spheres immersed in complex hyperquadric \(Q_3\). We firstly use Bahy-El-Dien and Wood’s results to obtain some characterizations of the harmonic sequences generated by conformal minimal immersions from \(S^2\) to \(G(2,5;\mathbb{R})\). Then we give a classification theorem of linearly full totally unramified conformal minimal immersions of constant curvature from \(S^2\) to \(G(2,5;\mathbb{R})\), or equivalently, a complex hyperquadric \(Q_3\).

Cited in 7 Documents

MSC:

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C55 Global differential geometry of Hermitian and Kählerian manifolds

Keywords:

conformal minimal immersion; Gauss curvature; Kähler angle; complex hyperquadric; classification
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\textit{M. Li} et al., J. Math. Soc. Japan 68, No. 2, 863--883 (2016; Zbl 1357.53069)
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