具有GTW Reeb Lie导数结构Jacobi算子的复二平面Grassmannian中的实超曲面
Real hypersurfaces in complex two-plane Grassmannians with GTW Reeb Lie derivative structure Jacobi operator
摘要：
利用推广的Tanaka-Webster联络，当结构Jacobi算子的GTW Reeb Lie导数与Reeb Lie导数重合时，考虑了复二平面Grassmannian $G_2({\mathbb C}^{m+2})$中的实超曲面$M$.然后利用同时对角化的方法，证明了满足这一条件的$G_2({\mathbb C}^{m+2})$中实超曲面的完全分类。在这种情况下，我们证明了$M$是一个开放的部分管周围的全测地$G_2({\mathbb C}^{m+1})$在$G_2({\mathbb C}^{m+2})$。
英文摘要：
Using generalized Tanaka-Webster connection, we considered a real hypersurface $M$ in a complex two-plane Grassmannian $G_2({\mathbb C}^{m+2})$ when the GTW Reeb Lie derivative of the structure Jacobi operator coincides with the Reeb Lie derivative. Next using the method of simultaneous diagonalization, we prove a complete classification for a real hypersurface in $G_2({\mathbb C}^{m+2})$ satisfying such a condition. In this case, we have proved that $M$ is an open part of a tube around a totally geodesic $G_2({\mathbb C}^{m+1})$ in $G_2({\mathbb C}^{m+2})$.
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