In this article, it is proved that there doesn’t exist any nonsingular holomorphic sphere in complex Grassmann manifold G（2, 5） with constant curvature k = 4/7, 1/2, 4/9. Thus, from [7] it follows that if φ ： S2 ...In this article, it is proved that there doesn’t exist any nonsingular holomorphic sphere in complex Grassmann manifold G（2, 5） with constant curvature k = 4/7, 1/2, 4/9. Thus, from [7] it follows that if φ ： S2 → G（2, 5） is a nonsingular holomorphic curve with constant curvature K, then, K = 4, 2, 4/3, 1 or 4/5.展开更多
In this paper, some construction theorems of pluriharmonic maps into complex Grassmann manifolds axe obtained. By these, there exists a characterization of strongly isotropic pluriharmonic maps.
We prove that if φ is a homogeneous harmonic map from a Riemann surface M into a complex Grassmann manifold G（k, n）, then the maps of the harmonic sequences generated by φ are all homogeneous.
In this paper, we construct a class of homogeneous minimal 2-spheres in complex Grassmann manifolds by applying the irreducible unitary representations of SU （2）. Furthermore, we compute induced metrics, Gaussian cu...In this paper, we construct a class of homogeneous minimal 2-spheres in complex Grassmann manifolds by applying the irreducible unitary representations of SU （2）. Furthermore, we compute induced metrics, Gaussian curvatures, Khler angles and the square lengths of the second fundamental forms of these homogeneous minimal 2-spheres in G（2, n ＋ 1） by making use of Veronese sequence.展开更多
1. Let S<sup>4</sup> be a four-sphere and let G<sub>2</sub>（TS<sup>4</sup>） be the Grassmann bundle on S<sup>4</sup> with natural Riemann metric and almost complex str...1. Let S<sup>4</sup> be a four-sphere and let G<sub>2</sub>（TS<sup>4</sup>） be the Grassmann bundle on S<sup>4</sup> with natural Riemann metric and almost complex structure. G<sub>2</sub>（TS<sup>4</sup>） is called （1, 2）-symplectic if the （1, 2）part of dk is zero where k is the K（?）hler form of G<sub>2</sub>（TS<sup>4</sup>）. In this note, we prove the following theorem:展开更多
In this paper, we are concerned with the classification of operators on complex separable Hilbert spaces, in the unitary equivalence sense and the similarity sense, respectively. We show that two strongly irreducible ...In this paper, we are concerned with the classification of operators on complex separable Hilbert spaces, in the unitary equivalence sense and the similarity sense, respectively. We show that two strongly irreducible operators A and B are unitary equivalent if and only if W＊（A＋B）′≈M2（C）, and two operators A and B in B1（Ω） are similar if and only if A′（AGB）/J≈M2（C）. Moreover, we obtain V（H^∞（Ω,μ）≈N and Ko（H^∞（Ω,μ）≈Z by the technique of complex geometry, where Ω is a bounded connected open set in C, and μ is a completely non-reducing measure on Ω.展开更多
基金Supported by the National Natural Science Foundation of China (10531090)Knowledge Innovation Funds of CAS (KJCX3-SYW-S03)
文摘In this article, it is proved that there doesn’t exist any nonsingular holomorphic sphere in complex Grassmann manifold G（2, 5） with constant curvature k = 4/7, 1/2, 4/9. Thus, from [7] it follows that if φ ： S2 → G（2, 5） is a nonsingular holomorphic curve with constant curvature K, then, K = 4, 2, 4/3, 1 or 4/5.
基金Research supported by National Nature Science Foundation of China(10171012),Tian Yuan Foundation 10226001 and Foundation of Southeast University
文摘In this paper, some construction theorems of pluriharmonic maps into complex Grassmann manifolds axe obtained. By these, there exists a characterization of strongly isotropic pluriharmonic maps.
基金This work was supported in part by the National Natural Science Foundation of China （Grant No. 11401481） and the Research Development Fund of XJTLU （Grant No. RDF13-01-14）.
文摘We prove that if φ is a homogeneous harmonic map from a Riemann surface M into a complex Grassmann manifold G（k, n）, then the maps of the harmonic sequences generated by φ are all homogeneous.
基金supported by the NSFC (11071248, 11071249)supported by the Fundamental Research Funds for the Central Universities(USTC)
文摘In this paper, we construct a class of homogeneous minimal 2-spheres in complex Grassmann manifolds by applying the irreducible unitary representations of SU （2）. Furthermore, we compute induced metrics, Gaussian curvatures, Khler angles and the square lengths of the second fundamental forms of these homogeneous minimal 2-spheres in G（2, n ＋ 1） by making use of Veronese sequence.
文摘1. Let S<sup>4</sup> be a four-sphere and let G<sub>2</sub>（TS<sup>4</sup>） be the Grassmann bundle on S<sup>4</sup> with natural Riemann metric and almost complex structure. G<sub>2</sub>（TS<sup>4</sup>） is called （1, 2）-symplectic if the （1, 2）part of dk is zero where k is the K（?）hler form of G<sub>2</sub>（TS<sup>4</sup>）. In this note, we prove the following theorem:
基金the 973 Project of China and the National Natural Science Foundation of China(Grant No.19631070)
文摘In this paper, we are concerned with the classification of operators on complex separable Hilbert spaces, in the unitary equivalence sense and the similarity sense, respectively. We show that two strongly irreducible operators A and B are unitary equivalent if and only if W＊（A＋B）′≈M2（C）, and two operators A and B in B1（Ω） are similar if and only if A′（AGB）/J≈M2（C）. Moreover, we obtain V（H^∞（Ω,μ）≈N and Ko（H^∞（Ω,μ）≈Z by the technique of complex geometry, where Ω is a bounded connected open set in C, and μ is a completely non-reducing measure on Ω.
