从S^2到CP^n的共形极小浸入(英文)

Conformal minimal immersions of S^2 in CP^n

通过李群、活动标架,以及调和映射来研究从S2到CPn的共形极小浸入.首先,用一种新方法证明Bolton的一个定理,从S2到CPn的全纯曲线在差一个刚动的情况下由度量唯一决定;其次,利用从S2到CPn的共形极小浸入来构造从S2到G2,n+1的共形极小浸入;最后,如果φ是从S2到CPn的全实共形极小浸入,且φ是常曲率的,则可以找出具体的等距变换g,使得gφ包含在RPnCPn中.

In this paper, conformal minimal 2-spheres immersed in a complex projective space are studied by applying Lie theory, moving frame and harmonic sequence. First, we use a different way from Bolton to prove that a holomorphic curve from S^2 into CPn is uniquely determined by its induced metric, up to a rigid motion. Secondly, via conformal minimal immersions of constant curvature from S^2 into CPn , we can construct new minimal immersions of S^2 in G2,n＋1, n ＋ 1 with constant curvature. Finally, if φ is a totally real conformal minimal 2-sphere of constant curvature immersed in a complex projective space, then we can find the explicit isometry transform g such that gφ lies in RP^n comprise CP^n.