|
|
|
Viewing Version
2
of
'symplectic manifold'
|
[ view 'symplectic manifold'
|
back to history
]
| Title of object: |
symplectic manifold |
| Canonical Name: |
SymplecticManifold |
| Type: |
Definition |
| Created on: |
2002-12-05 23:30:37.832864-05 |
| Modified on: |
2002-12-06 12:38:35.411003-05 |
| Classification: |
msc:53D05 |
| Defines: |
symplectic form |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here |
Content:
A {\em symplectic manifold} is a pair $(M,\omega)$ consisting of a smooth $2n$-manifold $M$ and a
closed \PMlinkname{2-form}{DifferentialForms} $\omega\in\Omega^2(M)$, which is non-degenerate
at each point. Equivalently, the $2n$-form $\omega^n$ is non-vanishing (the superscript denotes
powers of the wedge product). The differential form $\omega$ is often called a {\em symplectic
form}. |
|
|
|
|
|
