复Grassmann流形中的实迷向极小二维球面

Real isotropic minimal two-sphere in a complex Grassmann manifold

本文研究了复Grassmann流形中极小曲面的两种迷向性质之间的关系.首先给出了实迷向的定义,之后用整体微分形式刻画实迷向性质,然后介绍Calabi的线丛上的联络理论作为主要计算方法,最终运用调和序列理论证明复迷向性质强于实迷向.作为应用,本文证明了复射影空间中的极小二维球面是实强迷向的.

In this paper, we study the real isotropic minimal two-sphere immersed in a complex Grassmann manifold. Firstly, we define the real isotropic property and give equivalence definition in terms of global differential forms. Then we introduce Calabi＇s theory of connections on the line bundles as our main calculation method,finally we show that holomorphic isotropic is stronger than real isotropic. As an application of this result, we show that minimal two-sphere in a complex projective space is real strongly isotropic.