Minimal two-spheres with constant curvature in ℍ{\mathrm{P}}^n

Abstract

We study conformal minimal two-spheres immersed into the quaternionic projective space ℍ{\mathrm{P}}^n by using the twistor map. We present a method to construct new minimal two-spheres with constant curvature in ℍ{\mathrm{P}}^n, based on the minimal property and horizontal condition of Veronese map in complex projective space. Then we construct some concrete examples of conformal minimal two-spheres in ℍ{\mathrm{P}}^n with constant curvature 2/n, n = 4, 5, 6, respectively. Finally, we prove that there exist conformal minimal two-spheres with constant curvature 2/n in ℍ{\mathrm{P}}^n (n≥7):

Keywords

Quaternionic projective space / twistor map / minimal two-spheres / Veronese sequence

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2021 Higher Education Press