Abstract In this paper we first introduce the full expression of the curvature tensor of a real hypersurface M in complex hyperbolic two-plane Grassmannians S U 2 , m ∕ S ( U 2 ⋅ U m ) from the equation of Gauss and derive a new formula for the Ricci tensor of M in S U 2 , m ∕ S ( U 2 ⋅ U m ) . Finally we give a complete classification for Hopf real hypersurfaces in complex hyperbolic two-plane Grassmannians S U 2 , m ∕ S ( U 2 ⋅ U m ) with harmonic curvature or harmonic Weyl tensor.

中文翻译：

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复双曲两平面 Grassmannians 中实超曲面的调和曲率

摘要 在本文中，我们首先从高斯方程引入复双曲双平面格拉斯曼函数 SU 2 , m ∕ S ( U 2 ⋅ U m ) 中实超曲面 M 的曲率张量的完整表达式，并推导出一个新的公式： SU 2 中 M 的 Ricci 张量，m ∕ S (U 2 ⋅ U m)。最后，我们给出了具有调和曲率或调和 Weyl 张量的复双曲双平面 Grassmannians SU 2 , m ∕ S ( U 2 ⋅ U m ) 中的 Hopf 实超曲面的完整分类。