On conformal minimal immersions with constant curvature from two-spheres into the complex hyperquadrics

Hong Li () and Xiaoxiang Jiao ()
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Hong Li: Yunnan Normal University
Xiaoxiang Jiao: University of Chinese Academy of Sciences

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 4, 980-995

Abstract: Abstract In this paper, firstly we study the geometry of conformal minimal two-spheres immersed in the complex hyperquadric $$Q_{n-2}$$ Q n - 2 . Then we classify the linearly full irreducible conformal minimal immersions with constant curvature from $$S^2$$ S 2 to $$Q_{n-2}$$ Q n - 2 ( $$n\geqslant 7$$ n ⩾ 7 ) of isotropy order $$r=n-6$$ r = n - 6 under some conditions, which shows that all such immersions can be expressed by Veronese surfaces in $$\mathbb {C}P^{n-1}$$ C P n - 1 only under some conditions.

Keywords: Conformal minimal surface; Isotropy order; Constant curvature; Linearly full; 53C42; 53C55 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00308-8

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