TY - JOUR
T1 - On conformal minimal 2-spheres in complex Grassmann manifold G(2,n)
AU - Fei, Jie
AU - Jiao, Xiaoxiang
AU - Xu, Xiaowei
N1 - Funding Information:
The authors would like to thank the referee for making useful comments and suggestions. This project is supported by the NSFC (No. 11071248, No. 11071249), the Knowledge Innovation Program of the Chinese Academy of Sciences (KJCX3-SYW-SO3) and the Fundamental Research Funds for the Central Universities (USTC). The author, Xu would like to thank Professors Sen Hu, Qing Chen, Xiuxiong Chen and Bin Xu for their constant encouragement, and together with Fei would like to express appreciation to Professor Chiakuei Peng (Jiagui Peng) for his helpful guidance.
PY - 2011/5
Y1 - 2011/5
N2 - For a harmonic map f from a Riemann surface into a complex Grassmann manifold, Chern and Wolfson [4] constructed new harmonic maps ∂ f and -∂ f through the fundamental collineations ∂ and -∂ respectively. In this paper, we study the linearly full conformal minimal immersions from S2 into complex Grassmannians G(2, n), according to the relationships between the images of ∂ f and -∂ f .We obtain various pinching theorems and existence theorems about the Gaussian curvature, Kähler angle associated to the given minimal immersions, and characterize some immersions under special conditions. Some examples are given to show that the hypotheses in our theorems are reasonable.
AB - For a harmonic map f from a Riemann surface into a complex Grassmann manifold, Chern and Wolfson [4] constructed new harmonic maps ∂ f and -∂ f through the fundamental collineations ∂ and -∂ respectively. In this paper, we study the linearly full conformal minimal immersions from S2 into complex Grassmannians G(2, n), according to the relationships between the images of ∂ f and -∂ f .We obtain various pinching theorems and existence theorems about the Gaussian curvature, Kähler angle associated to the given minimal immersions, and characterize some immersions under special conditions. Some examples are given to show that the hypotheses in our theorems are reasonable.
KW - Function of analytic type
KW - Gaussian curvature
KW - Kähler angle
UR - http://www.scopus.com/inward/record.url?scp=79959229109&partnerID=8YFLogxK
U2 - 10.1007/s12044-011-0019-6
DO - 10.1007/s12044-011-0019-6
M3 - Article
AN - SCOPUS:79959229109
SN - 0253-4142
VL - 121
SP - 181
EP - 199
JO - Proceedings of the Indian Academy of Sciences: Mathematical Sciences
JF - Proceedings of the Indian Academy of Sciences: Mathematical Sciences
IS - 2
ER -