本書是一部英文版的學術專著，中文書名可譯為《拉格朗日幾何和哈密頓幾何：力學的應用》。本書的一個研究物件是拉杜·米龍首創的，如果說相近的，可能是Kahler流形。在當代數學的研究中，複流形的幾何變得越來越重要了，特別是Kahler流形，所謂的Kahler流形是一個具有在典型複結構的作用下不變的黎曼度量的複流形，同時它的典型複結構在相應的黎曼聯絡下又是平行的。
因此，Kahler流形是一類特殊的黎曼流形，具有更加豐富的幾何結構，從而具有更加豐富多彩的幾何性質。當然，Kahler流形可以從代數幾何的角度進行研究，而且它是代數幾何的主角，但是從微分幾何的角度來瞭解它的幾何結構和特徵是十分重要的，也是研究Kahler流形的基礎。
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$ 251 | 拉格朗日幾何和哈密頓幾何：力學的應用(英文)
作者：（羅）拉杜·米龍 出版社：哈爾濱工業大學出版社 出版日期：2021-10-01 語言：簡體中文 規格：平裝 / 256頁 / 13 x 19 x 1.28 cm / 普通級/ 1-1  博客來 - 數學
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圖書名稱：拉格朗日幾何和哈密頓幾何：力學的應用(英文)
內容簡介
目錄
1 The Geometry of tangent manifold
1.1 The manifold TM
1.2 Semisprays on the manifold TM
1.3 Nonlinear connections
1.4 N-linear connections
1.5 Parallelism.Structure equations
2 Lagrange spaces
2.1 The notion of Lagrange space
2.2 Variational problem.Euler-Lagrange equations
2.3 Canonical semispray.Nonlinear connection
2.4 Hamilton-Jacobi equations
2.5 Metrical N-linear connections
2.6 The electromagnetic and gravitational fields
2.7 The almost Kahlerian model of a Lagrange space Ln
2.8 Generalized Lagrange spaces
3 Finsler Spaces
3.1 Finsler metrics
3.2 Geodesics
3.3 Cartan nonlinear connection
3.4 Cartan metrical connection
4 The Geometry of Cotangent Manifold
4.1 Cotangent bundle
4.2 Variational problem.Hamilton-Jacobi equations
4.3 Nonlinear connections
4.4 N-linear connections
4.5 Parallelism,paths and structure equations
5 Hamilton spaces
5.1 Notion of Hamilton space
5.2 Nonlinear connection of a Hamilton space
5.3 The canonical metrical connection of Hamilton space Hn
5.4 Generalized Hamilton Spaces GHn
5.5 The almost Kahlerian model of a Hamilton space
6 Cartan spaces
6.1 Notion of Caftan space
6.2 Canonical nonlinear connection of Ln
6.3 Canonical metrical connection of Ln
6.4 The duality between Lagrange and Hamilton spaces
7 The Geometry of the manifold TkM
7.1 The bundle of acceleration of order k≥1
7.2 The Liouville vector fields
7.3 Variational Problem
7.4 Semisprays.Nonlinear connections
7.5 The dual coefficients of a nonlinear connection
7.6 Prolongation to the manifold TkM of the Riemannian structures given on the base manifold M
7.7 N-linear connections on TkM
8 Lagrange Spaces of Higher-order
8.1 The spaces L(k)n=(M,L)
8.2 Examples of spaces L(k)n
8.3 Canonical metrical N-connection
8.4 The Riemannian (k-1)n-contact model of the space L(k)n
8.5 The generalized Lagrange spaces of order k
9 Higher-Order Finsler spaces
9.1 Notion of Finsler space of order k
10 The Geometry of k-cotangent bundle
10.1 Notion of k-cotangent bundle,T*kM
11 Riemannian mechanical systems
11.1 Riemannian mechanical systems
11.2 Examples of Riemannian mechanical systems
11.3 The evolution semispray of the mechanical system ΣR
11.4 The nonlinear connection of ΣR
11.5 The canonical metrical connection CΓ(N)
11.6 The electromagnetism in the theory of the Riemannian mechanical systems ΣR
11.7 The almost Hermitian model of the RMS ΣR
12 Finslerian Mechanical systems
12.1 Semidefinite Finsler spaces
12.2 The notion of Finslerian mechanical system
12.3 The evolution semispray of the system ΣF
12.4 The canonical nonlinear connection of the Finslerian mechanical systems ΣF
12.5 The dynamical derivative determined by the evolution nonlinear connection N
12.6 Metric N-linear connection of ΣF
12.7 The electromagnetism in the theory of the Finslerian mechanical systems ΣF
12.8 The almost Hermitian model on the tangent manifold TM of the Finslerian mechanical systems ΣF
13 Lagrangian Mechanical systems
13.1 Lagrange Spaces.Preliminaries
13.2 Lagrangian Mechanical systems,ΣL
13.3 The evolution semispray of ΣL
13.4 The evolution nonlinear connection of ΣL
13.5 Canonical N-metrical connection of ΣL.Structure equations
13.6 Electromagnetic field
13.7 The almost Hermitian model of the Lagrangian mechanical system ΣL
13.8 Generalized Lagrangian mechanical systems
14 Hamiltonian and Cartanian mechanical systems
14.1 Hamilton spaces.Preliminaries
14.2 The Hamiltonian mechanical systems
14.3 Canonical nonlinear connection of ΣH
14.4 The Cartan mechanical systems
15 Lagrangian,Finslerian and Hamiltonian mechanical systems of order k≥1
15.1 Lagrangian Mechanical systems of order k≥1
15.2 Lagrangian mechanical system of order k,ΣLk
編輯手記
1.1 The manifold TM
1.2 Semisprays on the manifold TM
1.3 Nonlinear connections
1.4 N-linear connections
1.5 Parallelism.Structure equations
2 Lagrange spaces
2.1 The notion of Lagrange space
2.2 Variational problem.Euler-Lagrange equations
2.3 Canonical semispray.Nonlinear connection
2.4 Hamilton-Jacobi equations
2.5 Metrical N-linear connections
2.6 The electromagnetic and gravitational fields
2.7 The almost Kahlerian model of a Lagrange space Ln
2.8 Generalized Lagrange spaces
3 Finsler Spaces
3.1 Finsler metrics
3.2 Geodesics
3.3 Cartan nonlinear connection
3.4 Cartan metrical connection
4 The Geometry of Cotangent Manifold
4.1 Cotangent bundle
4.2 Variational problem.Hamilton-Jacobi equations
4.3 Nonlinear connections
4.4 N-linear connections
4.5 Parallelism,paths and structure equations
5 Hamilton spaces
5.1 Notion of Hamilton space
5.2 Nonlinear connection of a Hamilton space
5.3 The canonical metrical connection of Hamilton space Hn
5.4 Generalized Hamilton Spaces GHn
5.5 The almost Kahlerian model of a Hamilton space
6 Cartan spaces
6.1 Notion of Caftan space
6.2 Canonical nonlinear connection of Ln
6.3 Canonical metrical connection of Ln
6.4 The duality between Lagrange and Hamilton spaces
7 The Geometry of the manifold TkM
7.1 The bundle of acceleration of order k≥1
7.2 The Liouville vector fields
7.3 Variational Problem
7.4 Semisprays.Nonlinear connections
7.5 The dual coefficients of a nonlinear connection
7.6 Prolongation to the manifold TkM of the Riemannian structures given on the base manifold M
7.7 N-linear connections on TkM
8 Lagrange Spaces of Higher-order
8.1 The spaces L(k)n=(M,L)
8.2 Examples of spaces L(k)n
8.3 Canonical metrical N-connection
8.4 The Riemannian (k-1)n-contact model of the space L(k)n
8.5 The generalized Lagrange spaces of order k
9 Higher-Order Finsler spaces
9.1 Notion of Finsler space of order k
10 The Geometry of k-cotangent bundle
10.1 Notion of k-cotangent bundle,T*kM
11 Riemannian mechanical systems
11.1 Riemannian mechanical systems
11.2 Examples of Riemannian mechanical systems
11.3 The evolution semispray of the mechanical system ΣR
11.4 The nonlinear connection of ΣR
11.5 The canonical metrical connection CΓ(N)
11.6 The electromagnetism in the theory of the Riemannian mechanical systems ΣR
11.7 The almost Hermitian model of the RMS ΣR
12 Finslerian Mechanical systems
12.1 Semidefinite Finsler spaces
12.2 The notion of Finslerian mechanical system
12.3 The evolution semispray of the system ΣF
12.4 The canonical nonlinear connection of the Finslerian mechanical systems ΣF
12.5 The dynamical derivative determined by the evolution nonlinear connection N
12.6 Metric N-linear connection of ΣF
12.7 The electromagnetism in the theory of the Finslerian mechanical systems ΣF
12.8 The almost Hermitian model on the tangent manifold TM of the Finslerian mechanical systems ΣF
13 Lagrangian Mechanical systems
13.1 Lagrange Spaces.Preliminaries
13.2 Lagrangian Mechanical systems,ΣL
13.3 The evolution semispray of ΣL
13.4 The evolution nonlinear connection of ΣL
13.5 Canonical N-metrical connection of ΣL.Structure equations
13.6 Electromagnetic field
13.7 The almost Hermitian model of the Lagrangian mechanical system ΣL
13.8 Generalized Lagrangian mechanical systems
14 Hamiltonian and Cartanian mechanical systems
14.1 Hamilton spaces.Preliminaries
14.2 The Hamiltonian mechanical systems
14.3 Canonical nonlinear connection of ΣH
14.4 The Cartan mechanical systems
15 Lagrangian,Finslerian and Hamiltonian mechanical systems of order k≥1
15.1 Lagrangian Mechanical systems of order k≥1
15.2 Lagrangian mechanical system of order k,ΣLk
編輯手記
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