Real Hypersurfaces in Complex Two-Plane Grassmannians Whose Jacobi Operators Corresponding to -Directions are of Codazzi Type

We prove the non-existence of Hopf real hypersurfaces in complex two-plane Grassmannians whose Jacobi operators or the Jacobi corresponding to the directions in the distribution are of Codazzi type if they satisfy a further condition. We obtain that that they must be either of type (A) or of type (B) (see [2]), but no one of these satisfies our condition. As a consequence, we obtain the non-existence of Hopf real hypersurfaces in such ambient spaces whose Jacobi operators corresponding to -directions are parallel with the same further condition.

Hopf Hypersurfaces in Complex Two-Plane Grassmannians with Generalized Tanaka–Webster D-Parallel Shape Operator

In this paper, we consider a new notion of generalized Tanaka Webster З-parallel shape operator for a real hypersurface in a complex two-plane Grassrnannian and prove a non-existence theorem of a real hypersurface.

Commuting Structure Jacobi Operator for Real Hypersurfaces in Complex Two-plane Grassmannians

We classify real hypersurfaces in complex two-plane Grassmannians whose structure Jacobi operator commutes either with any other Jacobi operator or with the normal Jacobi operator.

ON PSEUDO-HOLOMORHPIC CURVESIN COMPLEX GRASSMANNIANS

Further geometry and topology for pseudo-holomorphic curves in complex Grassmannians Gm(CN) are studied. Some curvature pinching theorems for pseudo- holomorphic curyes with constant Kahler angles in Gm(CN) are obtained, so that the corresponding results for pseudoholomorphic curves in complex projective spaces are generalized.

Totally real minimal surfaces in complex Grassmannians

Given a harmonic map φfrom a Riemann surface M into the complex projectivespace CP^n, by using the -transform associated to the map φ, Chern et al. obtained the se-quence of harmonic maps. We call it a harmonic sequence. We will say that a harmonicmap φ: M→CP^n is k-orthogonal if k consecutive maps in the harmonic sequence of φ aremutually orthogonal. In particular, φis conformal if and only if φ is 3-orthogonal and, inall cases, φ is at most (n+1)-orthogonal. There are two possible ways in which the

G_(n,2)的Witten复形的同调群

通过研究实Grassmann流形Gn,2的Witten复形,给出了该复形的同调群的具体公式.根据Witten复形的基本结论可知,Gn,2的Witten复形的同调群恰是Gn,2的整系数奇异同调群.

G_(5,2)的同调群

利用Witten复形计算了实Grassmann流形G5,2的同调群,从而给出该方法的一个非平凡的例子.

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。