Structure of minimal 2-spheres of constant curvature in the complex hyperquadric

被引：2
|
作者：
Chi, Quo-Shin [1 ]
Xie, Zhenxiao [2 ]
Xu, Yan [3 ]
机构：
[1] Washington Univ, Dept Math & Stat, St Louis, MO 63130 USA
[2] China Univ Min & Technol Beijing, Dept Math, Beijing 100083, Peoples R China
[3] Peking Univ, Beijing Int Ctr Math Res, Beijing 100871, Peoples R China
来源：
ADVANCES IN MATHEMATICS | 2021年 / 391卷
关键词：
Hyperquadric; Holomorphic; 2-spheres; Minimal; Constant curvature; Singular-value decomposition; CLASSIFICATION; IMMERSIONS;
D O I：
10.1016/j.aim.2021.107967
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, the singular-value decomposition theory of complex matrices is explored to study constantly curved 2-spheres minimal in both CPn and the hyperquadric of CPn. The moduli space of all those noncongruent ones is introduced, which can be described by certain complex symmetric matrices modulo an appropriate group action. Using this description, many examples, such as constantly curved holomorphic 2-spheres of higher degree, nonhomogenous minimal 2-spheres of constant curvature, etc., are constructed. Uniqueness is proven for the totally real constantly curved 2-sphere minimal in both the hyperquadric and CPn. (C) 2021 Elsevier Inc. All rights reserved.
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页数：34
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