In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3. Under the assumptions that the globally null warped ...In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3. Under the assumptions that the globally null warped product manifold has no points with the same constant sectional curvature c as the Lorentzian ambient, we show that such isometric immersion splits into warped product of isometric immersions.展开更多
In this paper, a new approach to analyze synchronization of linearly coupled map lattices （LCMLs） is presented. A reference vector x（t） is introduced as the projection of the trajectory of the coupled system on th...In this paper, a new approach to analyze synchronization of linearly coupled map lattices （LCMLs） is presented. A reference vector x（t） is introduced as the projection of the trajectory of the coupled system on the synchronization manifold. The stability analysis of the synchronization manifold can be regarded as investigating the difference between the trajectory and the projection. By this method, some criteria are given for both local and global synchronization. These criteria indicate that the left and right eigenvectors corresponding to the eigenvalue ＂0＂ of the coupling matrix play key roles in the stability of synchronization manifold for the coupled system. Moreover, it is revealed that the stability of synchronization manifold for the coupled system is different from the stability for dynamical system in usual sense. That is, the solution of the coupled system does not converge to a certain knowable s（t） satisfying s（tT1） = f（s（t）） but to the reference vector on the synchronization manifold, which in fact is a certain weighted average of each x^i（t） for i=1,……, m, but not a solution s（t） satisfying s（t ＋ 1）=f（s（t））.展开更多
文摘In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3. Under the assumptions that the globally null warped product manifold has no points with the same constant sectional curvature c as the Lorentzian ambient, we show that such isometric immersion splits into warped product of isometric immersions.
基金Project supported by the National Natural Science Foundation of China (No. 60374018, No. 60574044)the Graduate Student Innovation Foundation of Fudan University.
文摘In this paper, a new approach to analyze synchronization of linearly coupled map lattices （LCMLs） is presented. A reference vector x（t） is introduced as the projection of the trajectory of the coupled system on the synchronization manifold. The stability analysis of the synchronization manifold can be regarded as investigating the difference between the trajectory and the projection. By this method, some criteria are given for both local and global synchronization. These criteria indicate that the left and right eigenvectors corresponding to the eigenvalue ＂0＂ of the coupling matrix play key roles in the stability of synchronization manifold for the coupled system. Moreover, it is revealed that the stability of synchronization manifold for the coupled system is different from the stability for dynamical system in usual sense. That is, the solution of the coupled system does not converge to a certain knowable s（t） satisfying s（tT1） = f（s（t）） but to the reference vector on the synchronization manifold, which in fact is a certain weighted average of each x^i（t） for i=1,……, m, but not a solution s（t） satisfying s（t ＋ 1）=f（s（t））.
