Riemannian Geometry of Contact and Symplectic Manifolds, 2 Edition
Second Edition features new material in most chapters, but particularly in Chapters 3, 7, and 12 Covers major new topics, such as a complex geodesic flow and the accompanying geometry of the projectivized holomorphic tangent bundle Features improvements and general corrections based off of the first edition throughout the text Intended for a broad audience of mathematicians, researchers and students in Riemannian geometry
Symplectic geometry is a central topic of current research in mathematics. Indeed, symplectic methods are key ingredients in the study of dynamical systems, differential equations, algebraic geometry, topology, mathematical physics and representations of Lie groups. This book is a true introduction to symplectic geometry, assuming only a general background in analysis and familiarity with linear algebra. It starts with the basics of the geometry of symplectic vector spaces. Then, symplectic manifolds are defined and explored.
Multiplicity diagrams can be viewed as schemes for describing the phenomenon of "symmetry breaking" in quantum physics. The subject of this book is the multiplicity diagrams associated with the classical groups U(n), O(n), etc. It presents such topics as asymptotic distributions of multiplicities, hierarchical patterns in multiplicity diagrams, lacunae, and the multiplicity diagrams of the rank 2 and rank 3 groups. The authors take a novel approach, using the techniques of symplectic geometry.
Symplectic Geometry (London Mathematical Society Lecture Note Series)
The area of symplectic geometry has developed rapidly in the past ten years with major new discoveries that were motivated by and have provided links with many other subjects such as dynamical systems, topology, gauge theory, mathematical physics, and singularity theory. The contributions to this volume reflect the richness of the subject and include expository papers as well as original research.
