复双平面格拉斯曼中实超曲面的*-Ricci张量

*-Ricci tensors for real hypersurfaces in complex hyperbolic two-plane Grassmannians

主要考虑在复双曲双面格拉斯曼SU2,m/S(U2U m),m≥2中的实超曲面的复曲率张量中引入*-Ricci张量。我们首先证明了SU2,m/S(U2U m)的Hopf超曲面上不存在*-Einstein度量。作为*-Einstein度量的一个推广,我们引入了*-Ricci孤立子,并证明了一个具有*-Ricci孤立子的实超曲面的位势场是Reeb矢量场,是SU2,m/S(U2U m)中全测地子流行SU2,m-1/S(U2U m-1)管状领域的一部分或者是一个无穷远处的中心是奇异的极限球面。最后,我们研究了一个具有伪反交换*-Ricci张量的Hopf超曲面。

It introduces the*-Ricci tensor from the curvature tensor of a real hypersurface in complex hyperbolic two-plane Grassmannian SU2,m/S(U 2U m),m≥2.It first prove that there do not exist *-Einstein metrics on Hopf hypersurfaces of SU2,m/S(U2U m).As a generalization of the*-Einstein metric,it introduces the*-Ricci soliton and prove that a real hypersurface with a*-Ricci soliton whose potential vector field is the Reeb vector field,is an open part of a tube around some totally geodesic SU2,m-1/S(U2U m-1)in SU2,m/S(U2U m)or a horosphere whose center at infinity is singular.Finally it studies a Hopf hypersurface with pseudo anti-commuting*-Ricci tensor.