The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem--the first such treatment in a book in English. Next comes a detaile...(展开全部)

This volume introduces techniques and theorems of Riemannian geometry, and opens the way to advanced topics. The text combines the geometric parts of Riemannian geometry with analytic aspects of the theory, and reviews recent research. The updated second edition includes a new coordinate-free formula that is easily remembered (the Koszul formula in disguise); an expanded number...(展开全部)

Riemannian Geometry is an expanded edition of a highly acclaimed and successful textbook (originally published in Portuguese) for first-year graduate students in mathematics and physics. The author's treatment goes very directly to the basic language of Riemannian geometry and immediately presents some of its most fundamental theorems. It is elementary, assuming only a modest b...(展开全部)

本书是仅见的全面而能与研究的前沿衔接的黎曼几何教材。是学习黎曼几何的必读书目。美国的大学，如几何学中心之一，石溪大学的数学系，本书就是黎曼几何方向博士生必须要掌握的。 遗憾的是本书某些论证过于简明，建议和do Carmo的《黎曼几何》互相参照。

Intended for a one year course, this volume serves as a single source, introducing students to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few works to combine both the geometric parts of Riemannian geometry and the analytic aspect...(展开全部)

Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of...(展开全部)

Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structur...(展开全部)

Why and how do social and cultural anthropologists make comparisons? What problems do they encounter in doing so, and how might these be resolved? What, if anything, makes one comparison better than another? This book answers these questions by exploring the many ways in which, from the nineteenth century to the present day, comparative methods have been conceptualised and re-i...(展开全部)