《黎曼几何与几何分析》(Riemannian Geometry and Geometric Analysis)(Jurgen Jost)4th[PDF]
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简介:
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这本书我在我的另一个资源里发过，现在单独拿出来发一次。初学黎曼几何的读者可以去这里看看：http://www.VeryCD.com/topics/2817268/
这部书是Springer出版社Universitext系列的一本，过后我会整理UT的书发到VC上来。
这是一本关于黎曼几何，尤其是几何分析的优秀教材，但是书中关于纯黎曼几何的讲述很简洁，不太适合初学者，书中很大篇幅在讲几何分析的基本方法，适合对黎曼几何已经有一定了解想从分析方面深入研究的读者。
这是书中部分前言：
Riemannian geometry is characterized, and research is oriented towards and shaped by concepts (geodesics, connections, curvature, ...) and objectives, in particular to understand certain classes of (compact) Riemannian manifolds defined by curvature conditions (constant or positive or negative curvature, ...). By way of contrast, geometric analysis is a perhaps somewhat less systematic collection of techniques, for solving extremal problems naturally arising in geometry and for investigating and characterizing their solutions. It turns out that the two fields complement each other very well; geometric analysis offers tools for solving difficult problems in geometry, and Riemannian geometry stimulates progress in geometric analysis by setting ambitious goals.
It is the aim of this book to be a systematic and comprehensive introduction to Riemannian geometry and a representative introduction to the methods of geometric analysis. It attempts a synthesis of geometric and analytic methods in the study of Riemannian manifolds.
/thumb.jpg)
这本书我在我的另一个资源里发过，现在单独拿出来发一次。初学黎曼几何的读者可以去这里看看：http://www.VeryCD.com/topics/2817268/
这部书是Springer出版社Universitext系列的一本，过后我会整理UT的书发到VC上来。
这是一本关于黎曼几何，尤其是几何分析的优秀教材，但是书中关于纯黎曼几何的讲述很简洁，不太适合初学者，书中很大篇幅在讲几何分析的基本方法，适合对黎曼几何已经有一定了解想从分析方面深入研究的读者。
这是书中部分前言：
Riemannian geometry is characterized, and research is oriented towards and shaped by concepts (geodesics, connections, curvature, ...) and objectives, in particular to understand certain classes of (compact) Riemannian manifolds defined by curvature conditions (constant or positive or negative curvature, ...). By way of contrast, geometric analysis is a perhaps somewhat less systematic collection of techniques, for solving extremal problems naturally arising in geometry and for investigating and characterizing their solutions. It turns out that the two fields complement each other very well; geometric analysis offers tools for solving difficult problems in geometry, and Riemannian geometry stimulates progress in geometric analysis by setting ambitious goals.
It is the aim of this book to be a systematic and comprehensive introduction to Riemannian geometry and a representative introduction to the methods of geometric analysis. It attempts a synthesis of geometric and analytic methods in the study of Riemannian manifolds.