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Donaldson's Q-operators for symplectic manifolds
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作者 LU Wen MA Xiaonan MARINESCU George 《Science China Mathematics》 SCIE CSCD 2017年第6期1047-1056,共10页
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
关键词 Q-operator QUANTIZATION symplectic manifold
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Lefschetz decomposition for de Rham cohomology on weakly Lefschetz symplectic manifolds
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作者 Qiang TAN Haifeng XU 《Frontiers of Mathematics in China》 SCIE CSCD 2015年第5期1169-1178,共10页
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.
关键词 symplectic manifold s-Lefschetz Lefschetz decomposition s-dd-lemma
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On the Geometrical Meaning of the Dynamic Equations in Analytical Mechanics
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作者 刘书振 陈书勤 王惠民 《Chinese Quarterly Journal of Mathematics》 CSCD 1993年第3期66-70,共5页
In this paper,the modern geometrical structure of analytical mechanics,the exterior differential forms and the geometrical meaning of dynamic equations are briefly discussed.
关键词 FIBRE tangent and cotangent bundles symplectic manifolds riemannian kinemic metric integral manifolds
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Generalized Birkhofflan representation of nonholonomic systems and its discrete variational algorithm 被引量:3
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作者 刘世兴 刘畅 +1 位作者 花巍 郭永新 《Chinese Physics B》 SCIE EI CAS CSCD 2016年第11期346-352,共7页
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
关键词 variational preserving coordinates constraints adjoint satisfy manifold transformed preserve symplectic
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INVARIANT FORM AND INTEGRAL INVARIANTS ON KAHLER MANIFOLD
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作者 张荣业 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第2期269-278,共10页
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
关键词 Kahler manifold symplectic manifold invariant form integral invariant vector field form field Lie derivative exterior differential
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A Finite-Dimensional Completely Integrable System Associated with Boussinesq Hierarchy
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作者 CHEN Lan-Xin ZHANG Jun-Xian 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第12期1081-1086,共6页
In this paper, a new completely integrable system related to the complex spectral problem -φ xx+(i/4)wpx+(i/4)(wp)x+(1/4)vφ=iλφxand the constrained flows of the Boussinesq equations axe generated. Accor... In this paper, a new completely integrable system related to the complex spectral problem -φ xx+(i/4)wpx+(i/4)(wp)x+(1/4)vφ=iλφxand the constrained flows of the Boussinesq equations axe generated. According to the viewpoint of Hamiltonian mechanics, the Euler-Lagrange equations and the Legendre transformations, a reasonable Jacobi-Ostrogradsky coordinate system is obtained. Moreover, by means of the constrained conditions between the potentiaJ u, v and the eigenfunction φ, the involutive representations of the solutions for the Boussinesq equation hieraxchy axe given. 展开更多
关键词 eigenvalue problem constraint flow symplectic manifold completely integrability involutive representation
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A Recursive Basis for Primitive Forms in Symplectic Spaces and Applications to Heisenberg Groups
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作者 Annalisa BALDI Marilena BARNABEI Bruno FRANCHI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2016年第3期265-285,共21页
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
关键词 symplectic manifolds differential forms Heisenberg groups combinatorial functions
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Stabilization of 4-manifolds
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作者 CHO YongSeung 《Science China Mathematics》 SCIE 2014年第9期1835-1840,共6页
The complex surface X obtained by 8 points blown up on CP2 and Barlow’s surface Y are homeomorphic,but not diffeomorphic.Using the Gromov-Witten invariant Ruan showed that the stabilized manifolds X×S2and Y×... The complex surface X obtained by 8 points blown up on CP2 and Barlow’s surface Y are homeomorphic,but not diffeomorphic.Using the Gromov-Witten invariant Ruan showed that the stabilized manifolds X×S2and Y×S2are not deformation equivalent.In this note,we show that the stabilized manifolds X×S1and Y×S1are diffeomorphic and non-deformation equivalent in cosymplectic sense. 展开更多
关键词 cosymplectic manifold symplectic manifold Gromov-Witten invariant h-cobordism Whitehead group DEFORMATION
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Topological recursion relations on M_(3,2) 被引量:2
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作者 KIMURA Takashi LIU Xiaobo 《Science China Mathematics》 SCIE CSCD 2015年第9期1909-1922,共14页
We give some new genus-3 universal equations for Gromov-Witten invariants of compact symplectic manifolds. These equations were obtained by studying relations in the tautological ring of the moduli space of2-pointed g... We give some new genus-3 universal equations for Gromov-Witten invariants of compact symplectic manifolds. These equations were obtained by studying relations in the tautological ring of the moduli space of2-pointed genus-3 stable curves. A byproduct of our search for genus-3 equations is a new genus-2 universal equation for Gromov-Witten invariants. 展开更多
关键词 Gromov-Witten invariants universal equations symplectic manifolds
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Symmetric Periodic Orbits and Uniruled Real Liouville Domains
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作者 Urs FRAUENFELDER Otto van KOERT 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2016年第4期607-624,共18页
A real Liouville domain is a Liouville domain with an exact anti-symplectic involution. The authors call a real Liouville domain uniruled if there exists an invariant finite energy plane through every real point. Asym... A real Liouville domain is a Liouville domain with an exact anti-symplectic involution. The authors call a real Liouville domain uniruled if there exists an invariant finite energy plane through every real point. Asymptotically, an invariant finite energy plane converges to a symmetric periodic orbit. In this note, they work out a criterion which guarantees uniruledness for real Liouville domains. 展开更多
关键词 Symmetric periodic orbits Real symplectic manifolds Real uniruledness
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FEEDBACK REALIZATION OF HAMILTONIAN SYSTEMS 被引量:1
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作者 CHENGDaizhan XIZairong 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2002年第1期61-68,共8页
This paper investigates the relationship between state feedback and Hamiltonian realization. First, it is proved that a completely controllable linear system always has a state feedback state equation Hamiltonian real... This paper investigates the relationship between state feedback and Hamiltonian realization. First, it is proved that a completely controllable linear system always has a state feedback state equation Hamiltonian realization. Necessary and sufficient conditions are obtained for it to have a Hamiltonian realization with natural output. Then some conditions for an affine nonlinear system to have a Hamiltonian realization are given. For generalized outputs, the conditions of the feedback, keeping Hamiltonian, are discussed. Finally, the admissible feedback controls for generalized Hamiltonian systems are considered. 展开更多
关键词 Hamiltonianrealization symplectic group symplectic manifold Poisson bracket generalized Hamiltonian systems.
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Discreteness of Flux Groups 被引量:1
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作者 Yong Seung CHO Myung Im LIM 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2006年第1期115-122,共8页
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
关键词 symplectic diffeomorphisms FLUX symplectically aspherical manifold Donaldson submanifold
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