An introduction to symplectic geometry,
Hamilton systems and complex geometry
Rainer Schimming
Schimming
Rainer
Institute of physics publishing Szczecin 2002,
Rainer Schimming

**Preprint series:**
Institute of physics publishing Szczecin 2002,

**MSC 2000**

- 53D05 Symplectic manifolds, general

**Abstract**

The aim of the paper is to tell theoretical physicists some important mathematical topics and to be, in this framework, as didactical as possible.

From a modern point of view, a great deal of physics - parts of mechanics as well as of field theory - turns out to be a kind of
differential geometry, namely {\it symplectic geometry} or, slightly
more generally, {\it Poisson geometry}. {\it Hamilton systems} are described
in terms of this scheme. Geometry is the true nature of the
"canonical formalism" in mechanics and field theory. {\it Complex
geometry} and {\it almost complex geometry} are close in spirit to
symplectic geometry. Moreover, these kinds of geometries became
important in Yang-Mills theory, string theory and other areas of
theoretical physics. For these reasons, we introduce into Poisson
geometry, symplectic geometry, Hamilton systems, almost complex
geometry, and complex geometry in one text.

The reader is supposed to know fundamentals of linear algebra, analytic geometry, and differential geometry.

*This document is well-formed XML.*