Riemannian Geometry (Translations of Mathematical Monographs) by Takashi Sakai (PDF)

Description

This volume is an English translation of Sakai’s textbook on Riemannian geometry which was originally written in Japanese and published in 1992. The author’s intent behind the original book was to provide to advanced undergraduate and graduate students an introduction to modern Riemannian geometry that could also serve as a reference. The book begins with an explanation of the fundamental notion of Riemannian geometry. Special emphasis is placed on understandability and readability, to guide students who are new to this area. The remaining chapters deal with various topics in Riemannian geometry, with the main focus on comparison methods and their applications.

User’s Reviews

Editorial Reviews: From the Inside Flap A good source for teaching a somewhat advanced class in differential geometry and certainly contains enough material for a one-year course. [It is] also a good source for the working differential geometer…a fine book and worthwhile addition to any differential geometer’s library. Bulletin of the American Mathematical Society

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐”Riemannian Geometry” by Sakai is a wonderful book for a second course in Riemannian Geometry, especially if your interest is in global Riemannian geometry. For example, his presentation of the topology of compact manifolds of positive curvature is delightful; banishing the proof of 1/4-pinched injectivity radius to the appendix, he presents wonderfully geometric proofs of the 1/4-pinched sphere theorem and the generalized sphere theorem. Also, all the tools that one could want to do global Riemannian geometry are here: Rauch, Toponogov, Bishop-Gromov, etc. I sometimes felt that he sacrifices some clarity for needless(?) generality (e.g., a very lengthy proof of Ambrose’s theorem so that he can state it with once broken geodesics), but this is a minor complaint. Sakai generally does a great job of filling in all of the details and of selecting proofs that are geometrically motivated. He includes an extensive bibliography, and each chapter ends with “Notes on the References” to guide you in the literature. A final advantage for self-study is a fair number of exercises scattered throughout, with hints and solutions for numerous of these.

⭐The book is the paperback reissue of the original hardcover. It has a wealth of material on the global differential geometry, isoperimetric inequalities, properties of the laplace operator, and comparison theorems, both in presentation and in problem sets. The text is clear and perhaps the most lucid out of the most books on the subject that I had a chance to learn from. The reason is that the author wrote the book having concrete applications in mind. Unfortunately, most of the differential geometry books either describe applications, such as texts by Yau, Berger, or Cheeger; or focus on foundations and present plenty of abstract symbol manipulation, such as Kobayashi-Nomizu, Bishop-Crittenden, etc. Sakai offers a balanced text which helps students to confidently know most of the classical results on the subject. For example, Sakai text is thorough enough to include the discussion of the orthonormal frame bundles. Overall, the book is definitely a worthy addition to one’s library.

Keywords

Free Download Riemannian Geometry (Translations of Mathematical Monographs) in PDF format
Riemannian Geometry (Translations of Mathematical Monographs) PDF Free Download
Download Riemannian Geometry (Translations of Mathematical Monographs) 1996 PDF Free
Riemannian Geometry (Translations of Mathematical Monographs) 1996 PDF Free Download
Download Riemannian Geometry (Translations of Mathematical Monographs) PDF
Free Download Ebook Riemannian Geometry (Translations of Mathematical Monographs)