论文信息 - An introduction to symplectic geometry - 字舞流文

An introduction to symplectic geometry

A symplectic form on a vector space V is a skew-symmetric bilinear form α: V × V → R such that \( \tilde \alpha :V \to V^ \star \tilde \alpha (x)(y) = \alpha (x,y) \) is an isomorphism. Here V* denotes the dual of V.

Augustin Banyaga | A. Banyaga

[1] Augustin Banyaga,et al. Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique , 1978 .

[2] J. Moser. On the volume elements on a manifold , 1965 .

[3] V. I. Arnol'd,et al. Characteristic class entering in quantization conditions , 1967 .

[4] M. Berger,et al. Differential Geometry: Manifolds, Curves, and Surfaces , 1987 .

[5] L. Polterovich,et al. Hamiltonian diffeomorphisms and lagrangian distributions , 1992 .

[6] E. Zehnder. Remarks on Periodic Solutions on Hypersurfaces , 1987 .

[7] J. Duistermaat. On the Morse index in variational calculus , 1976 .

[8] Ralph Abraham,et al. Foundations Of Mechanics , 2019 .

[9] V. Arnold. The Sturm theorems and symplectic geometry , 1985 .

[10] L. Polterovich. Monotone Lagrange submanifolds of linear spaces and the Maslov class in cotangent bundles , 1991 .

[11] Alan Weinstein,et al. Lectures on Symplectic Manifolds , 1977 .

[12] M. Audin. Classes caracteristiques lagrangiennes , 1987 .

[13] I. Vaisman. Symplectic Geometry and Secondary Characteristic Classes , 1987 .

[14] Jean-Luc Brylinski,et al. A differential complex for Poisson manifolds , 1988 .

[15] Jerrold E. Marsden,et al. Review: Victor Guillemin and Shlomo Sternberg, Geometric asymptotics, and Nolan R. Wallach, Symplectic geometry and Fourier analysis , 1979 .

[16] Shlomo Sternberg,et al. Geometric Asymptotics, Revised edition , 1977 .