| 书目名称 | Symplectic Geometry | | 副标题 | An Introduction base | | 编辑 | B. Aebischer,M. Borer,H. M. Reimann | | 视频video | | | 丛书名称 | Progress in Mathematics | | 图书封面 |  | | 描述 | 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 1Iaslov 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 | | 出版日期 | Book 1994 | | 关键词 | contact geometry; differential geometry; manifold; symplectic geometry; topology | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-0348-7512-7 | | isbn_softcover | 978-3-0348-7514-1 | | isbn_ebook | 978-3-0348-7512-7Series ISSN 0743-1643 Series E-ISSN 2296-505X | | issn_series | 0743-1643 | | copyright | Springer Basel AG 1994 |
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发表于 2025-3-21 16:25:50
