We prove an estimate for Donaldson's Q-operator on a prequantized compact symplectic manifold.This estimate is an ingredient in the recent result of Keller and Lejmi(2017) about a symplectic generalization of Dona...We prove an estimate for Donaldson's Q-operator on a prequantized compact symplectic manifold.This estimate is an ingredient in the recent result of Keller and Lejmi(2017) about a symplectic generalization of Donaldson's lower bound for the L^2-norm of the Hermitian scalar curvature.展开更多
For a compact symplectic manifold which is s-Lefschetz which is weaker than the decomposition for de hard Lefschetz property, we prove that the Lefschetz Rham cohomology also holds.
The important notions and results of the integral invariants of Poincard and Cartan-Poincard and the relationship between integral invariant and invariant form established first by E. Cartan in the classical mechanics...The important notions and results of the integral invariants of Poincard and Cartan-Poincard and the relationship between integral invariant and invariant form established first by E. Cartan in the classical mechanics are generalized to Hamilton mechanics on Kiihler manifold, by the theory of modern geometry and advanced calculus, to get the corresponding wider arid deeper results. differential展开更多
By using the discrete variational method,we study the numerical method of the general nonholonomic system in the generalized Birkhoffian framework,and construct a numerical method of generalized Birkhoffian equations ...By using the discrete variational method,we study the numerical method of the general nonholonomic system in the generalized Birkhoffian framework,and construct a numerical method of generalized Birkhoffian equations called a self-adjoint-preserving algorithm.Numerical results show that it is reasonable to study the nonholonomic system by the structure-preserving algorithm in the generalized Birkhoffian framework.展开更多
This paper is divided in two parts： in Section 2, we define recursively a privileged basis of the primitive forms in a symplectic space（V^（2n）, ω）. Successively, in Section 3, we apply our construction in the se...This paper is divided in two parts： in Section 2, we define recursively a privileged basis of the primitive forms in a symplectic space（V^（2n）, ω）. Successively, in Section 3, we apply our construction in the setting of Heisenberg groups H^n, n ≥ 1, to write in coordinates the exterior differential of the so-called Rumin＇s complex of differential forms in H^n.展开更多
Let （M, ω） be a closed symplectic 2n-dimensional manifold. Donaldson in his paper showed that there exist 2m-dimensional symplectie submanifolds （V^2m,ω） of （M,ω）, 1 ≤m ≤ n - 1, with （m - 1）-equivalent in...Let （M, ω） be a closed symplectic 2n-dimensional manifold. Donaldson in his paper showed that there exist 2m-dimensional symplectie submanifolds （V^2m,ω） of （M,ω）, 1 ≤m ≤ n - 1, with （m - 1）-equivalent inclusions. On the basis of this fact we obtain isomorphic relations between kernel of Lefschetz map of M and kernels of Lefschetz maps of Donaldson submanifolds V^2m, 2 ≤ m ≤ n - 1. Then, using this relation, we show that the flux group of M is discrete if the action of π1 （M） on π2（M） is trivial and there exists a retraction r ： M→ V, where V is a 4-dimensional Donaldson submanifold. And, in the symplectically aspherical case, we investigate the flux groups of the manifolds.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11401232 and 11528103)Agence nationale de la recherche(Grant No.ANR-14-CE25-0012-01)funded through the Institutional Strategy of the University of Cologne within the German Excellence Initiative and Deutsche Forschungsgemeinschaft Funded Project Sonderforschungsbereich Transregio 191
文摘We prove an estimate for Donaldson's Q-operator on a prequantized compact symplectic manifold.This estimate is an ingredient in the recent result of Keller and Lejmi(2017) about a symplectic generalization of Donaldson's lower bound for the L^2-norm of the Hermitian scalar curvature.
基金Acknowledgements The authors were very grateful to their advisor Prof. Hongyu Wang for discussion and suggestions. This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11371309, 11471145, 11401514）, the University Science Research Project of Jiangsu Province （14KJB110027）, and the Foundation of Yangzhou University （2014CXJ004）.
文摘For a compact symplectic manifold which is s-Lefschetz which is weaker than the decomposition for de hard Lefschetz property, we prove that the Lefschetz Rham cohomology also holds.
文摘The important notions and results of the integral invariants of Poincard and Cartan-Poincard and the relationship between integral invariant and invariant form established first by E. Cartan in the classical mechanics are generalized to Hamilton mechanics on Kiihler manifold, by the theory of modern geometry and advanced calculus, to get the corresponding wider arid deeper results. differential
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11472124,11572145,11202090,and 11301350)the Doctor Research Start-up Fund of Liaoning Province,China(Grant No.20141050)+1 种基金the China Postdoctoral Science Foundation(Grant No.2014M560203)the General Science and Technology Research Plans of Liaoning Educational Bureau,China(Grant No.L2013005)
文摘By using the discrete variational method,we study the numerical method of the general nonholonomic system in the generalized Birkhoffian framework,and construct a numerical method of generalized Birkhoffian equations called a self-adjoint-preserving algorithm.Numerical results show that it is reasonable to study the nonholonomic system by the structure-preserving algorithm in the generalized Birkhoffian framework.
基金Supported by University of Bolognafunds for selected research topics+1 种基金supported by the Gruppo Nazionale per l’Analisi Matematica,la Probabilita e le loro Applicazioni(GNAMPA)of the Istituto Nazionale di Alta Matematica(INdA M)supported by P.R.I.N.of M.I.U.R.,Italy
文摘This paper is divided in two parts： in Section 2, we define recursively a privileged basis of the primitive forms in a symplectic space（V^（2n）, ω）. Successively, in Section 3, we apply our construction in the setting of Heisenberg groups H^n, n ≥ 1, to write in coordinates the exterior differential of the so-called Rumin＇s complex of differential forms in H^n.
文摘Let （M, ω） be a closed symplectic 2n-dimensional manifold. Donaldson in his paper showed that there exist 2m-dimensional symplectie submanifolds （V^2m,ω） of （M,ω）, 1 ≤m ≤ n - 1, with （m - 1）-equivalent inclusions. On the basis of this fact we obtain isomorphic relations between kernel of Lefschetz map of M and kernels of Lefschetz maps of Donaldson submanifolds V^2m, 2 ≤ m ≤ n - 1. Then, using this relation, we show that the flux group of M is discrete if the action of π1 （M） on π2（M） is trivial and there exists a retraction r ： M→ V, where V is a 4-dimensional Donaldson submanifold. And, in the symplectically aspherical case, we investigate the flux groups of the manifolds.
