Symplectic and Poisson structures on loop spaces of smooth manifolds, and integrable systems-猫眼课题宝

光滑流形环空间上的辛结构和泊松结构以及可积系统

DOI：

发表时间：

1998

期刊：

影响因子：

通讯作者：

中科院分区：

文献类型：

作者：

Олег Иванович Мохов

第一章.第一节光滑流形的loop空间上的辛结构的微分几何§ 1.1.光滑流形的loop空间上的辛结构和Poisson结构。基本定义§ 1.2.伪黎曼流形和具有挠率的二维非线性sigma模型的循环空间上的一阶齐次辛结构§ 1.3.退化拉格朗日系统的辛和泊松结构§ 1.4.几乎辛和辛流形的回路空间上的二阶齐次辛结构和辛联络§ 1.5.光滑流形的圈空间上的齐次型复形及其上同调群第二章.微分几何类型的局部和非局部泊松结构§ 2.1.流体动力学型多维局部泊松结构的黎曼几何§ 2.2.流体动力学类型的哈密顿系统和常黎曼曲率度量§ 2.3.流体动力学型非齐次哈密顿系统§ 2.4.常黎曼曲率空间上的Killing-Poisson双向量和广义海森堡磁体的双哈密顿结构§ 2.5.微分几何型齐次Poisson结构二维拓扑场论中的结合性方程和流体力学型不可对角化可积系统§ 3.1。结合性方程作为流体动力学类型的不可对角化可积齐次系统§ 3.2。结合性方程的泊松和辛结构§ 3.3.任意发展系统限制于其非退化积分的驻点集的正则哈密顿表示定理及其在结合性方程和流体动力学型系统中的应用

ContentsIntroduction Chapter I. Differential geometry of symplectic structures on loop spaces of smooth manifolds § 1.1. Symplectic and Poisson structures on loop spaces of smooth manifolds. Basic definitions § 1.2. Homogeneous symplectic structures of the first order on loop spaces of pseudo-Riemannian manifolds and two-dimensional non-linear sigma-models with torsion § 1.3. Symplectic and Poisson structures of degenerate Lagrangian systems § 1.4. Homogeneous symplectic structures of the second order on loop spaces of almost symplectic and symplectic manifolds and symplectic connections § 1.5. Complexes of homogeneous forms on loop spaces of smooth manifolds and their cohomology groupsChapter II. Local and non-local Poisson structures of differential-geometric type § 2.1. Riemannian geometry of multidimensional local Poisson structures of hydrodynamic type § 2.2. Hamiltonian systems of hydrodynamic type and metrics of constant Riemannian curvature § 2.3. Non-homogeneous Hamiltonian systems of hydrodynamic type § 2.4. Killing-Poisson bivectors on spaces of constant Riemannian curvature and bi-Hamiltonian structure of the generalized Heisenberg magnets § 2.5. Homogeneous Poisson structures of differential-geometric typeChapter III. The equations of associativity in two-dimensional topological field theory and non-diagonalizable integrable systems of hydrodynamic type § 3.1. Equations of associativity as non-diagonalizable integrable homogeneous systems of hydrodynamic type § 3.2. Poisson and symplectic structures of the equations of associativity § 3.3. Theorem on a canonical Hamiltonian representation of the restriction of an arbitrary evolution system to the set of stationary points of its non-degenerate integral and its applications to the equations of associativity and systems of hydrodynamic type Bibliography

Symplectic and Poisson structures on loop spaces of smooth manifolds, and integrable systems

光滑流形环空间上的辛结构和泊松结构以及可积系统

文献摘要

被引文献

相似文献