TY - JOUR
T1 - Equivariant totally real 3-spheres in the complex projective space C{double-struck}P{double-struck} n
AU - Fei, Jie
AU - Peng, Chiakuei
AU - Xu, Xiaowei
N1 - Funding Information:
This project is supported by the NSFC (Grant Nos. 11071249 , 11101389 ), the Fundamental Research Funds for the Central Universities (USTC) and Anhui Provincial Natural Science Foundation (No. 1208085MA01 ). The authors would like to thank the refereeʼs comments.
PY - 2012/6
Y1 - 2012/6
N2 - In this paper we study the equivariant totally real immersions from S 3 into C{double-struck}P{double-struck} n. We first reduce these immersions to a system of algebraic equations by the unitary representations of SU(2). We give some explicit examples of minimal totally real isometric immersions from S3/m(m+2)3 into C{double-struck}P{double-struck} n, and characterize the minimal totally real isometric immersions from S3/m(m+2)3 into C{double-struck}P{double-struck} n by the standard example. We also give many minimal linearly full isometric immersions from S1/53 into C{double-struck}P{double-struck} 7, C{double-struck}P{double-struck} 11 and C{double-struck}P{double-struck} 15. As an application of our method, we classify equivariant Lagrangian S 3 in C{double-struck}P{double-struck} 3 again.
AB - In this paper we study the equivariant totally real immersions from S 3 into C{double-struck}P{double-struck} n. We first reduce these immersions to a system of algebraic equations by the unitary representations of SU(2). We give some explicit examples of minimal totally real isometric immersions from S3/m(m+2)3 into C{double-struck}P{double-struck} n, and characterize the minimal totally real isometric immersions from S3/m(m+2)3 into C{double-struck}P{double-struck} n by the standard example. We also give many minimal linearly full isometric immersions from S1/53 into C{double-struck}P{double-struck} 7, C{double-struck}P{double-struck} 11 and C{double-struck}P{double-struck} 15. As an application of our method, we classify equivariant Lagrangian S 3 in C{double-struck}P{double-struck} 3 again.
KW - Constant sectional curvature
KW - Equivariant totally real immersions
KW - Lagrangian submanifolds
UR - http://www.scopus.com/inward/record.url?scp=84859754022&partnerID=8YFLogxK
U2 - 10.1016/j.difgeo.2012.04.002
DO - 10.1016/j.difgeo.2012.04.002
M3 - Article
AN - SCOPUS:84859754022
SN - 0926-2245
VL - 30
SP - 262
EP - 273
JO - Differential Geometry and its Application
JF - Differential Geometry and its Application
IS - 3
ER -