Conformal minimal immersions with constant curvature from S² to Q₅

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

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