Conformal minimal two-spheres in Q ₂

Abstract

In this paper, we consider a conformal minimal immersion f from S ₂ into a hyperquadric Q ₂, and prove that its Gaussian curvature K and normal curvature K ^⊥ satisfy K + K ^⊥ = 4. We also show that the ellipse of curvature is a circle.

Keywords

Complex hyperquadric / Gaussian curvature / normal curvature / minimal immersion / ellipse of curvature

References

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