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 propose a new method for smoothly interpolating a given set of data points on Grassmann and Stiefel manifolds using a generalization of the De Casteljau algorithm.To that end,we reduce interpolation problem to the ...We propose a new method for smoothly interpolating a given set of data points on Grassmann and Stiefel manifolds using a generalization of the De Casteljau algorithm.To that end,we reduce interpolation problem to the classical Euclidean setting,allowing us to directly leverage the extensive toolbox of spline interpolation.The interpolated curve enjoy a number of nice properties:The solution exists and is optimal in many common situations.For applications,the structures with respect to chosen Riemannian metrics are detailed resulting in additional computational advantages.展开更多
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
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
Based on the relationship between symplectic group Sp（2） and （2）, we provide an intuitive explanation （model） of the 3-dimensional Lagrangian Grassmann manifold （2）, the singular cycles of （2）, and the speci...Based on the relationship between symplectic group Sp（2） and （2）, we provide an intuitive explanation （model） of the 3-dimensional Lagrangian Grassmann manifold （2）, the singular cycles of （2）, and the special Lagrangian Grassmann manifold S（2）. Under this model, we give a formula of the rotation paths defined by Arnold.展开更多
In this article, we analyse three related preconditioned steepest descent algorithms, which are partially popular in Hartree-Fock and Kohn-Sham theory as well as invariant subspace computations, from the viewpoint of ...In this article, we analyse three related preconditioned steepest descent algorithms, which are partially popular in Hartree-Fock and Kohn-Sham theory as well as invariant subspace computations, from the viewpoint of minimization of the corresponding functionals, constrained by orthogonality conditions. We exploit the geometry of the admissible manifold, i.e., the invariance with respect to unitary transformations, to reformulate the problem on the Grassmann manifold as the admissible set. We then prove asymptotical linear convergence of the algorithms under the condition that the Hessian of the corresponding Lagrangian is elliptic on the tangent space of the Grassmann manifold at the minimizer.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.
文摘We propose a new method for smoothly interpolating a given set of data points on Grassmann and Stiefel manifolds using a generalization of the De Casteljau algorithm.To that end,we reduce interpolation problem to the classical Euclidean setting,allowing us to directly leverage the extensive toolbox of spline interpolation.The interpolated curve enjoy a number of nice properties:The solution exists and is optimal in many common situations.For applications,the structures with respect to chosen Riemannian metrics are detailed resulting in additional computational advantages.
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.
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The author is grateful to Professor Yiming Long for his interest and Professor Xijun Hu for many useful advises and patient guidance. Also, the author would like to convey thanks to the anonymous referees for useful comments and suggestions. Finally, the author won＇t forget his beloved friends and family members, for their understanding and endless love through the duration of his studies. This work was partially supported by the National Natural Science Foundation of China （Grant No. 11425105）.
文摘Based on the relationship between symplectic group Sp（2） and （2）, we provide an intuitive explanation （model） of the 3-dimensional Lagrangian Grassmann manifold （2）, the singular cycles of （2）, and the special Lagrangian Grassmann manifold S（2）. Under this model, we give a formula of the rotation paths defined by Arnold.
基金supported by the DFG SPP 1445:"Modern and universal first-principles methods for many-electron systems in chemistry and physics" and the EU NEST project BigDFT.
文摘In this article, we analyse three related preconditioned steepest descent algorithms, which are partially popular in Hartree-Fock and Kohn-Sham theory as well as invariant subspace computations, from the viewpoint of minimization of the corresponding functionals, constrained by orthogonality conditions. We exploit the geometry of the admissible manifold, i.e., the invariance with respect to unitary transformations, to reformulate the problem on the Grassmann manifold as the admissible set. We then prove asymptotical linear convergence of the algorithms under the condition that the Hessian of the corresponding Lagrangian is elliptic on the tangent space of the Grassmann manifold at the minimizer.
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.
