复Grassmann流形中全实曲面的构造

Construction of totally real surfaces in complex Grassmannians

给出复Grassmann流形G(2,n+2)的全实曲面的一种构造方法,也就是把G(2,n+2)看作HP^(n+1)中极小子流形Q^(n+1)的商,并证明G(2,n+2)中的曲面可以水平提升到Q^(n+1)中当且仅当它是全实的。

We present a construction of the complex Grassmannian G(2,n+2)as a quotient of some minimal submanifold Q^(n+1) of HP^(n+1),then show that a surface in G(2,n+2)can be horizontally lifted to Q^(n+1) if and only if it is totally real.