Requiring only an understanding of differentiable manifolds, Isaac Chavel covers introductory ideas followed by a selection of more specialized topics in this second edition. He provides a clearer treatment of many topics, with new proofs of some theorems and a new chapter on the Riemannian geometry of surfaces. Among the classical topics shown in a new setting is isoperimetric inequalities in curved spaces. Completely new themes created by curvature include the classical Rauch comparison theorem and its consequences in geometry and topology, and the interaction of microscopic behavior of the geometry with the macroscopic structure of the space.
Riemannian Geometry
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Book Description
Editorial Reviews
Review
"Each chapter concludes with an excellent section of notes and advanced exercises with further results, with hints and sketches of solutions at the end of the book...I think that it is the best reference on Riemannian geometry available, especially for someone interested in isoperimetric problems...Chavel is one of about a dozen mathematics books I keep at home for ready reference."
Frank Morgan, SIAM Review
Frank Morgan, SIAM Review
Book Description
This corrected and clarified second edition, including a new chapter on the Riemannian geometry of surfaces, provides an introduction to the geometry of curved spaces. Its main themes are the effect of the curvature of these spaces on the usual notions of classical Euclidean geometry and the new notions and ideas motivated by curvature itself. An ambitious Notes and Exercises section is included with each chapter. The book, which could be used as the basis for a graduate course, will appeal to graduate students and researchers in differential geometry and topology, analysis and differential equations.
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This review is from: Riemannian Geometry: A Modern Introduction (Cambridge Studies in Advanced Mathematics) (Paperback)
This book is excellent for students who want to be in contact with the research in this area. I recommend to everyone.
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Inside This Book
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First Sentence:
One cannot start discussing Riemannian geometry without mention of the classics. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Construct Fermi New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
One cannot start discussing Riemannian geometry without mention of the classics. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Construct Fermi New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Citations (learn more)
This book cites 63
books:
See all 63 books this book cites
14
books
cite this book:
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- Isoperimetric Inequalities: Differential Geometric and Analytic Perspectives (Cambridge Tracts in Mathematics) by Isaac Chavel in Front Matter, and Back Matter
- Differential Geometry (Proceedings of Symposia in Pure Mathematics ; V. 54 Part 1, 2, 3) (Pt.1-3) by Robert Greene in Back Matter (1), and Back Matter (2)
- Riemannian Geometry During the Second Half of the Twentieth Century (University Lecture Series) by Marcel Berger in Front Matter, and Back Matter
- Differential Geometry (Proceedings of Symposia in Pure Mathematics, vol. 27, pt. 2) by Shiing-Shen Chern in Back Matter (1), and Back Matter (2)
- Comparison Geometry (Mathematical Sciences Research Institute Publications) by Karsten Grove in Back Matter
See all 63 books this book cites
- Modern Spatiotemporal Geostatistics (International Association for Mathematical Geology: Studies in Mathematical Geology) by George Christakos in Back Matter
- Spectral Theory and Geometry (London Mathematical Society Lecture Note Series) by E. Brian Davies on page 132
- Riemannian Manifolds: An Introduction to Curvature (Graduate Texts in Mathematics) by John M. Lee in Back Matter
- Submanifolds and Holonomy (Research Notes in Mathematics Series) by Jurgen Berndt in Back Matter
- An Introduction to the Analysis of Paths on a Riemannian Manifold (Mathematical Surveys and Monographs) by Daniel W. Stroock in Back Matter
See all 14 books citing this book
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