几何Ⅵ

出版时间：2009-1  出版社：科学出版社  作者：波斯特尼科夫  页数：503  
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前言

　　要使我国的数学事业更好地发展起来，需要数学家淡泊名利并付出更艰苦地努力。另一方面，我们也要从客观上为数学家创造更有利的发展数学事业的外部环境，这主要是加强对数学事业的支持与投资力度，使数学家有较好的工作与生活条件，其中也包括改善与加强数学的出版工作。　　从出版方面来讲，除了较好较快地出版我们自己的成果外，引进国外的先进出版物无疑也是十分重要与必不可少的。从数学来说，施普林格（springer）出版社至今仍然是世界上最具权威的出版社。科学出版社影印一批他们出版的好的新书，使我国广大数学家能以较低的价格购买，特别是在边远地区工作的数学家能普遍见到这些书，无疑是对推动我国数学的科研与教学十分有益的事。　　这次科学出版社购买了版权，一次影印了23本施普林格出版社出版的数学书，就是一件好事，也是值得继续做下去的事情。大体上分一下，这23本书中，包括基础数学书5本，应用数学书6本与计算数学书12本，其中有些书也具有交叉性质。这些书都是很新的，2000年以后出版的占绝大部分，共计16本，其余的也是1990年以后出版的。这些书可以使读者较快地了解数学某方面的前沿，例如基础数学中的数论、代数与拓扑三本，都是由该领域大数学家编著的“数学百科全书”的分册。对从事这方面研究的数学家了解该领域的前沿与全貌很有帮助。按照学科的特点，基础数学类的书以“经典”为主，应用和计算数学类的书以“前沿”为主。这些书的作者多数是国际知名的大数学家，例如《拓扑学》一书的作者诺维科夫是俄罗斯科学院的院士，曾获“菲尔兹奖”和“沃尔夫数学奖”。这些大数学家的著作无疑将会对我国的科研人员起到非常好的指导作用。　　当然，23本书只能涵盖数学的一部分，所以，这项工作还应该继续做下去。更进一步，有些读者面较广的好书还应该翻译成中文出版，使之有更大的读者群。　　总之，我对科学出版社影印施普林格出版社的部分数学著作这一举措表示热烈的支持，并盼望这一工作取得更大的成绩。

内容概要

This book treats that part of Riemannian geometry related to more classical topics in a very original，clear and solid style.Before going to Riemannian geometry，the author presents a more general theory of manifolds with a linear connection.Having in mind different generalizations of Riemannian manifolds，it is clearly stressed which notions and theorems belong to Riemannian geometry and which of them are of a more general nature.Much attention is paid to transformation groups of smooth manifolds.    Throughout the book，different aspects of symmetric spaces are treated.The author successfully combines the co-ordinate and invariant approaches to differential geometry，which give the reader tools for practical calculations as well as a theoretical understanding of the subject.The book contains a very useful large appendix on foundations of differentiable manifolds and basic structures on them which makes it self-contained and practically independent from other sources.    The results are well presented and useful for students in mathematics and theoretical physics，and for experts in these fields.The book can serve as a textbook for students doing geometry，as well as a reference book for professional mathematicians and physicists.

书籍目录

PrefaceChapter 1.Affine ConnectionsChapter 2.Covariant Differentiation.CurvatureChapter 3.Affine Mappings.SubmanifoldsChapter 4.Structural Equations.Local SymmetriesChapter 5.Symmetric SpacesChapter 6.Connections on Lie GroupsChapter 7.Lie FunctorChapter 8.Affine Fields and Related TopicsChapter 9.Cartan TheoremChapter 10.Palais and Kobayashi TheoremsChapter 11.Lagrangians in Riemannian SpacesChapter 12.Metric Properties of GeodesicsChapter 13.Harmonic Functionals and Related TopicsChapter 14.Minimal SurfacesChapter 15.Curvature in Riemannian SpaceChapter 16.Gaussian CurvatureChapter 17.Some Special TensorsChapter 18.Surfaces with Conformal StructureChapter 19.Mappings and Submanifolds ⅠChapter 20.Submanifolds ⅡChapter 21.Fundamental Forms of a HypersurfaceChapter 22.Spaces of Constant CurvatureChapter 23.Space FormsChapter 24.Four-Dimensional ManifoldsChapter 25.Metrics on a Lie Group ⅠChapter 26.Metrics on a Lie Group ⅡChapter 27.Jacobi TheoryChapter 28.Some Additional Theorems ⅠChapter 29.Some Additional Theorems ⅡChapter 30.Smooth ManifoldsChapter 31.Tangent VectorsChapter 32.Submanifolds of a Smooth ManifoldChapter 33.Vector and Tensor Fields Differential FormsChapter 34.Vector BundlesChapter 35.Connections on Vector BundlesChapter 36.Curvature TensorSuggested ReadingIndex

用户评论 (总计3条)

•   About Riemannian Geom., this is a wonderful one to explain how it works. :)
•   几何Ⅵ黎曼几何,经典好书，得查字典呢
•   几何VI是科学出版社出版的国外数学名著中的一部,学术水平高,印刷纸张装帧好,堪称精品.