Introduction to Symplectic and Hamiltonian Geometry
by Ana Cannas da Silva
Number of pages: 158
This text covers foundations of symplectic geometry in a modern language. We start by describing symplectic manifolds and their transformations, and by explaining connections to topology and other geometries. Next we study hamiltonian fields, hamiltonian actions and some of their practical applications in the context of mechanics and dynamical systems. We assume previous knowledge of the geometry of smooth manifolds, though the main required facts are collected in appendices.
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by Hansjoerg Geiges - arXiv
This is an introductory text on the more topological aspects of contact geometry. After discussing some of the fundamental results of contact topology, I move on to a detailed exposition of the original proof of the Lutz-Martinet theorem.
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Tight and taut submanifolds form an important class of manifolds with special curvature properties, one that has been studied intensively by differential geometers since the 1950's. This book contains six articles by leading experts in the field.
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