S^4到CP^n的常曲率弱Lagrangian极小浸入  

Weakly Lagrangian Minimal Immersions of S^4 Into CP^n with Constant Curvature

作　　者：黎镇琦[1] 廖春艳[1] 

机构地区：[1]南昌大学数学系,南昌330031

出　　处：《数学学报（中文版）》2012年第2期369-384,共16页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10671087);天元青年基金(11026109);江西省自然科学基金资助项目(2009GZS0017)

摘　　要：研究球面S^4到CP^n的常曲率弱Lagrangian极小浸入■:S^4→CP^n.如果■的诱导度量ds^2具有常(截面)曲率c,则存在一个整数s≥1,使得c=4/[s(s+3)].浸入■被两个四元齐次多项式f_s和f_(s-1)唯一确定.当s=1,即c=1,或s=2,即c=2/5时,浸入■是绝对实的.The weakly Lagrangian minimal immersions with constant curvature from S4 into CPn are studied. It is proved that if the induced metric has constant curvature c, than c = 4/[s（s ＋ 3）] for some integer s 〉 1. And the immersion φ ： S4 → CPn is uniquely determined by two homogenous polynomials fs and fs-1 of four variables. If s = 1 or s = 2, or equivalently, if c = 1 or c = 2/5, the immersion φ is absolute real.

关 键 词：复射影空间 常曲率 弱Lagrangian极小浸入 

分 类 号：O186[理学—数学]