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Titlebook: Riemannian Geometry of Contact and Symplectic Manifolds; David E. Blair Book 20021st edition Springer Science+Business Media New York 2002

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發(fā)表于 2025-3-21 19:04:20 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱Riemannian Geometry of Contact and Symplectic Manifolds
編輯David E. Blair
視頻videohttp://file.papertrans.cn/831/830317/830317.mp4
叢書(shū)名稱Progress in Mathematics
圖書(shū)封面Titlebook: Riemannian Geometry of Contact and Symplectic Manifolds;  David E. Blair Book 20021st edition Springer Science+Business Media New York 2002
描述The author‘s lectures, "Contact Manifolds in Riemannian Geometry," volume 509 (1976), in the Springer-Verlag Lecture Notes in Mathematics series have been out of print for some time and it seems appropriate that an expanded version of this material should become available. The present text deals with the Riemannian geometry of both symplectic and contact manifolds, although the book is more contact than symplectic. This work is based on the recent research of the author, his students, colleagues, and other scholars, the author‘s graduate courses at Michigan State University and the earlier lecture notes. Chapter 1 presents the general theory of symplectic manifolds. Principal circle bundles are then discussed in Chapter 2 as a prelude to the Boothby- Wang fibration of a compact regular contact manifold in Chapter 3, which deals with the general theory of contact manifolds. Chapter 4 focuses on Rie- mannian metrics associated to symplectic and contact structures. Chapter 5 is devoted to integral submanifolds of the contact subbundle. In Chapter 6 we discuss the normality of almost contact structures, Sasakian manifolds, K- contact manifolds, the relation of contact metric structures
出版日期Book 20021st edition
關(guān)鍵詞Differential Geometry; Differential Topology; Manifolds; Riemannian geometry; curvature; manifold
版次1
doihttps://doi.org/10.1007/978-1-4757-3604-5
isbn_ebook978-1-4757-3604-5Series ISSN 0743-1643 Series E-ISSN 2296-505X
issn_series 0743-1643
copyrightSpringer Science+Business Media New York 2002
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沙發(fā)
發(fā)表于 2025-3-21 21:54:00 | 只看該作者
板凳
發(fā)表于 2025-3-22 03:41:26 | 只看該作者
地板
發(fā)表于 2025-3-22 07:43:26 | 只看該作者
5#
發(fā)表于 2025-3-22 12:03:07 | 只看該作者
3-Sasakian Manifolds,As with the last chapter we will give more of a survey and only a few proofs. Another survey of both history and recent work on 3-Sasakian manifolds is Boyer and Galicki [1999].
6#
發(fā)表于 2025-3-22 13:56:41 | 只看該作者
7#
發(fā)表于 2025-3-22 20:41:23 | 只看該作者
https://doi.org/10.1007/978-1-4757-3604-5Differential Geometry; Differential Topology; Manifolds; Riemannian geometry; curvature; manifold
8#
發(fā)表于 2025-3-22 23:35:59 | 只看該作者
Symplectic Manifolds,onal differentiable (..) manifold ..n together with a global 2-form Ω which is closed and of maximal rank, i.e., .Ω = 0, Ω. ≠ 0. By a .: (.., Ω.) → (.., Ω.) we mean a diffeomorphism . : .. → .. such that .*Ω. =Ω..
9#
發(fā)表于 2025-3-23 04:42:21 | 只看該作者
Contact Manifolds, manifold is orientable. Also . has rank 2. on the Grassmann algebra ∧ ... at each point . ∈ . and thus we have a 1-dimensional subspace, {. ∈ ...|.(...) = 0}, on which . ≠ 0 and which is complementary to the subspace on which . = 0. Therefore choosing .. in this subspace normalized by .(..) = 1 we have a global vector field . satisfying ..
10#
發(fā)表于 2025-3-23 08:50:43 | 只看該作者
Associated Metrics,rtant for our study; many of these were already mentioned in Chapter 1. For more detail the reader is referred to Gray and Hervella [1980] , Kobayashi-Nomizu [1963–69, Chapter IX] and Kobayashi-Wu [1983]; also, despite its classical nature, the book of Yano [1965] contains helpful information on many of these structures.
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