Classification of homogeneous holomorphic two-spheres in complex Grassmann manifolds

被引：4
|
作者：
Fei, Jie [1 ]
机构：
[1] Xian Jiaotong Liverpool Univ, Dept Math Sci, Suzhou 215123, Peoples R China
来源：
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2019年 / 62卷
关键词：
Homogeneous holomorphic two-spheres; Veronese surfaces; Gaussian curvature; The second fundamental form; HARMONIC MAPS; CONSTANT CURVATURE; CLASSICAL-SOLUTIONS; MINIMAL; 2-SPHERES; LIE-GROUPS; CONSTRUCTION; RIGIDITY; CURVES;
D O I：
10.1016/j.difgeo.2018.09.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we completely classify the linearly full homogeneous holomorphic two-spheres in the complex Grassmann manifolds G(2, N) and G(3, N). We also obtain the Gauss equation for the holomorphic immersions from a Riemann surface into G(k, N). By using which, we give explicit expressions of the Gaussian curvature and the square of the length of the second fundamental form of these homogeneous holomorphic two-spheres in G(2, N) and G(3, N). (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码：1 / 38
页数：38
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