Conformal minimal immersions with constant curvature from S~2 to Q_5

摘要

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 S-2 to G(2, 7; R); or equivalently, a complex hyperquadric Q(5) 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 S-2 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.