Geometric Aspects of the Einstein Equations and Integrable Systems

Inhaltsverzeichnis

• Exact solutions in gauge theory, general relativity, and their supersymmetric extensions.
• Symmetries and solutions of the einstein equations.
• Superposition of solutions in general relativity.
• Gauge fields, gravitation and Kaluza-Klein theory.
• Gravitational shock waves.
• Soliton surfaces and their applications (soliton geometry from spectral problems).
• Completely integrable systems of evolution equations on KAC moody lie algebras.
• Integrable lattice systems in two and three dimensions.
• Isovectors and prolongation structures by Vessiot's vector field formulation of partial differential equations.
• Hamiltonian flow on an energy surface: 240 years after the euler-maupertuis principle.