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Riemannian Geometry
 
Takashi Sakai Okayama University, Okayama, Japan
Riemannian Geometry
Softcover ISBN:  978-0-8218-0284-7
Product Code:  MMONO/149
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4105-0
Product Code:  MMONO/149.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Softcover ISBN:  978-0-8218-0284-7
eBook: ISBN:  978-1-4704-4105-0
Product Code:  MMONO/149.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
Riemannian Geometry
Click above image for expanded view
Riemannian Geometry
Takashi Sakai Okayama University, Okayama, Japan
Softcover ISBN:  978-0-8218-0284-7
Product Code:  MMONO/149
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4105-0
Product Code:  MMONO/149.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Softcover ISBN:  978-0-8218-0284-7
eBook ISBN:  978-1-4704-4105-0
Product Code:  MMONO/149.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
  • Book Details
     
     
    Translations of Mathematical Monographs
    Volume: 1491996; 358 pp
    MSC: Primary 53; 58; 35;

    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.

    The author has faithfully translated the Japanese edition with the exception of appendix 6—on the collapsing of Riemannian manifolds and Gromov's convergence theorem—which has been considerably revised and expanded, including the addition of a few comments on further developments and corrections of small errors.

    Readership

    Advanced undergraduate and graduate students interested in differential geometry.

  • Table of Contents
     
     
    • Chapters
    • Chapter I. Preliminaries from manifolds
    • Chapter II. Fundamental concepts in Riemannian geometry
    • Chapter III. Global concepts in Riemannian geometry
    • Chapter IV. Comparison theorems and applications
    • Chapter V. Curvature and topology of Riemannian manifolds
    • Chapter VI. Isoperimetric inequality and spectral geometry
    • Appendices
    • Hints and solutions to exercises and problems
    • Bibliography
  • Reviews
     
     
    • 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 AMS
    • This book on differential geometry packs into about 350 pages a great variety of topics—from the basics to spectral geometry and the topology of Riemannian manifolds ... A good text for a graduate course in which students are well-prepared and motivated ... should also be a very good reference for a practicing mathematician interested in Riemannian geometry ... touches on a great many subjects in addition to those it covers in detail.

      Mathematical Reviews
    • The book is well-written and will enable the reader to enter areas which are still in rapid progress. The author succeeds very well in explaining the fundamental concepts of Riemannian geometry and why the topics he deals with deserve the attention of the reader ... The book is a valuable addition to the literature and will be a good reference.

      Zentralblatt MATH
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1491996; 358 pp
MSC: Primary 53; 58; 35;

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.

The author has faithfully translated the Japanese edition with the exception of appendix 6—on the collapsing of Riemannian manifolds and Gromov's convergence theorem—which has been considerably revised and expanded, including the addition of a few comments on further developments and corrections of small errors.

Readership

Advanced undergraduate and graduate students interested in differential geometry.

  • Chapters
  • Chapter I. Preliminaries from manifolds
  • Chapter II. Fundamental concepts in Riemannian geometry
  • Chapter III. Global concepts in Riemannian geometry
  • Chapter IV. Comparison theorems and applications
  • Chapter V. Curvature and topology of Riemannian manifolds
  • Chapter VI. Isoperimetric inequality and spectral geometry
  • Appendices
  • Hints and solutions to exercises and problems
  • Bibliography
  • 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 AMS
  • This book on differential geometry packs into about 350 pages a great variety of topics—from the basics to spectral geometry and the topology of Riemannian manifolds ... A good text for a graduate course in which students are well-prepared and motivated ... should also be a very good reference for a practicing mathematician interested in Riemannian geometry ... touches on a great many subjects in addition to those it covers in detail.

    Mathematical Reviews
  • The book is well-written and will enable the reader to enter areas which are still in rapid progress. The author succeeds very well in explaining the fundamental concepts of Riemannian geometry and why the topics he deals with deserve the attention of the reader ... The book is a valuable addition to the literature and will be a good reference.

    Zentralblatt MATH
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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