In this paper, we study geometry of isometric minimal immersions of Riemannian surfaces in a symmetric space by moving frames and prove that the Gaussian curvature must be constant if the immersion is of parallel second fundamental form. In particular, when the surface is $S^2$, we discuss the special case and obtain a necessary and sufficient condition such that its second fundamental form is parallel. We alsoconsider isometric minimal two-spheres immersed in complex two-dimensional K?¤hlersymmetric spaces with parallel second fundamental form, and prove that the immersionis totally geodesic with constant K?¤hler angle if it is neither holomorphic nor antiholomorphicwith K?¤hler angle $alpha eq 0$ (resp. $alpha eq pi$) everywhere on $S^2$.
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机译：在本文中，我们通过移动框架研究了对称空间中黎曼曲面的等距最小浸入的几何形状，并证明了如果浸入具有平行的第二基本形式，则高斯曲率必须恒定。特别是，当表面为$ S ^ 2 $时，我们讨论特殊情况并获得必要和充分的条件，以使其第二基本形式平行。我们还考虑了浸没在具有平行第二基本形式的复杂二维K？äler对称空间中的等距极小两个球体，并证明了在K？hler角不是全纯或反全纯的情况下，浸没完全是具有恒定K？hler角的测地线$ S ^ 2 $上的$ alpha eq 0 $（分别是$ alpha eq pi $）。
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