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Symplectic Geometry - An Introduction based on the Seminar in Bern, 1992 (Paperback, Softcover reprint of the original 1st ed. 1994)
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Symplectic Geometry - An Introduction based on the Seminar in Bern, 1992 (Paperback, Softcover reprint of the original 1st ed. 1994)
Series: Progress in Mathematics, 124
Expected to ship within 10 - 15 working days
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The seminar Symplectic Geometry at the University of Berne in
summer 1992 showed that the topic of this book is a very active
field, where many different branches of mathematics come tog9ther:
differential geometry, topology, partial differential equations,
variational calculus, and complex analysis. As usual in such a
situation, it may be tedious to collect all the necessary
ingredients. The present book is intended to give the nonspecialist
a solid introduction to the recent developments in symplectic and
contact geometry. Chapter 1 gives a review of the symplectic group
Sp(n, R), sympkctic manifolds, and Hamiltonian systems (last but
not least to fix the notations). The 1\Iaslov index for closed
curves as well as arcs in Sp(n, R) is discussed. This index will be
used in chapters 5 and 8. Chapter 2 contains a more detailed
account of symplectic manifolds start ing with a proof of the
Darboux theorem saying that there are no local in variants in
symplectic geometry. The most important examples of symplectic
manifolds will be introduced: cotangent spaces and Kahler
manifolds. Finally we discuss the theory of coadjoint orbits and
the Kostant-Souriau theorem, which are concerned with the question
of which homogeneous spaces carry a symplectic structure."
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