Lagrangian submanifold LagrangianSubmanifold 2002-12-06 13:00:43 2006-10-25 00:18:42 Definition % 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 If $(M,\omega)$ is a \PMlinkname{symplectic $2n$-manifold}{SymplecticManifold}, then a submanifold $L$ is called {\em \PMlinkescapetext{Lagrangian}} if it is isotropic, and of dimension $n$. This is the maximal dimension an isotropic submanifold can have, by the non-degeneracy of $\omega$.