The Ricci Operator and Shape Operator of Real Hypersurfaces in a Non-Flat 2-Dimensional Complex Space Form

In this paper, we study a real hypersurface M in a non-at 2-dimensional complex space form M2(c) with η-parallel Ricci and shape operators. The characterizations of these real hypersurfaces are obtained.

Commuting Structure Jacobi Operator for Real Hypersurfaces in Complex Space Forms

Let M be a real hypersurface of a complex space form with almost contact metric structure (φ,ξ,η,g). In this paper, we prove that if the structure Jacobi operator Rξ=(·,ξ) ξ is φ▽ξξ-parallel and Rξ commute with the shape operator, then M is a Hopf hypersurface. Further, if Rξ is φ▽ξξ-parallel and Rξ commute with the Ricci tensor, then M is also a Hopf hypersurface provided that TrRξ is constant.

电压稳定控制参数空间下最近Hopf分岔边界的计算

提出寻求关键特征值的指标,给出发生Hopf分岔的初始负荷增长方向,由此保证求取的超平面的法向量和Hopf分岔的参数空间相对应。也提出了在参数空间下求取系统发生最近Hopf分岔点的迭代算法,使用该算法能得到趋近该点的最危险负荷增长方式。在每步迭代中,求取参数空间下Hopf分岔超平面的垂直向量,得到新的负荷增长方式,使之达到最近的Hopf分岔点。采用IEEE标准14节点系统及IEEE-30节点系统进行仿真计算,验证了该算法的有效性和收敛性。

On almost complex curves and Hopf hypersurfaces in the nearly Kahler six-sphere

We study the almost complex curves and Hopf hypersurfaces in the nearly Khler S6(1),and their relations.For Hopf hypersurfaces,we give a classification theorem under some additional conditions.For compact almost complex curves,we obtain some interesting global results with respect to Gaussian curvature,area and the genus.

复双平面格拉斯曼中实超曲面的*-Ricci张量

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。