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Mathematics: Theory and Applications Ser.: Riemannian Geometry by Manfredo Perdigáo Do Carmo (1992, Hardcover)
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Authors : Manfredo Perdigao do Carmo.
- Buy it nowRiemannian Geometry by Manfredo Perdigao do Carmo
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About this product
Product Identifiers
PublisherBirkhäuser Boston
ISBN-100817634908
ISBN-139780817634902
eBay Product ID (ePID)532581
Product Key Features
Number of PagesXv, 300 Pages
LanguageEnglish
Publication NameRiemannian Geometry
Publication Year1992
SubjectGeometry / Non-Euclidean, Geometry / Differential, Physics / Mathematical & Computational
TypeTextbook
Subject AreaMathematics, Science
AuthorManfredo Perdigáo Do Carmo
SeriesMathematics: Theory and Applications Ser.
FormatHardcover
Dimensions
Item Weight22.7 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Edition Number4
Intended AudienceScholarly & Professional
LCCN91-037377
Reviews"This is one of the best (if even not just the best) book for those who want to get a good, smooth and quick, but yet thorough introduction to modern Riemannian geometry." Publicationes Mathematicae"This is a very nice introduction to global Riemannian geometry, which leads the reader quickly to the heart of the topic. Nevertheless, classical results are also discussed on many occasions, and almost 60 pages are devoted to exercises." Newsletter of the EMS"In the reviewer's opinion, this is a superb book which makes learning a real pleasure."-Revue Romaine de Mathematiques Pures et Appliquees"This mainstream presentation of differential geometry serves well for a course on Riemannian geometry, and it is complemented by many annotated exercises." -Monatshefte F. Mathematik, "This is one of the best (if even not just the best) book for those who want to get a good, smooth and quick, but yet thorough introduction to modern Riemannian geometry." a?Publicationes Mathematicae "This is a very nice introduction to global Riemannian geometry, which leads the reader quickly to the heart of the topic. Nevertheless, classical results are also discussed on many occasions, and almost 60 pages are devoted to exercises." a?Newsletter of the EMS "In the reviewer's opinion, this is a superb book which makes learning a real pleasure." a?Revue Romaine de Mathematiques Pures et Appliquees "This mainstream presentation of differential geometry serves well for a course on Riemannian geometry, and it is complemented by many annotated exercises." a?Monatshefte F. Mathematik, "This is one of the best (if even not just the best) book for those who want to get a good, smooth and quick, but yet thorough introduction to modern Riemannian geometry." Publicationes Mathematicae "This is a very nice introduction to global Riemannian geometry, which leads the reader quickly to the heart of the topic. Nevertheless, classical results are also discussed on many occasions, and almost 60 pages are devoted to exercises." Newsletter of the EMS "In the reviewer's opinion, this is a superb book which makes learning a real pleasure." -Revue Romaine de Mathematiques Pures et Appliquees "This mainstream presentation of differential geometry serves well for a course on Riemannian geometry, and it is complemented by many annotated exercises." -Monatshefte F. Mathematik, "This is one of the best (if even not just the best) book for those who want to get a good, smooth and quick, but yet thorough introduction to modern Riemannian geometry." -Publicationes Mathematicae "This is a very nice introduction to global Riemannian geometry, which leads the reader quickly to the heart of the topic. Nevertheless, classical results are also discussed on many occasions, and almost 60 pages are devoted to exercises." -Newsletter of the EMS "In the reviewer's opinion, this is a superb book which makes learning a real pleasure." --Revue Romaine de Mathematiques Pures et Appliquees "This mainstream presentation of differential geometry serves well for a course on Riemannian geometry, and it is complemented by many annotated exercises." --Monatshefte F. Mathematik
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal516.3/73
Table Of Content0-Differentiable Manifolds.- 1-Riemannian Metrics.- 2-Affine Connections; Riemannian Connections.- 3-Geodesics; Convex Neighborhoods.- 4-Curvature.- 5-Jacobi Fields.- 6-Isometric Immersions.- 7-Complete Manifolds; Hopf-Rinow and Hadamard Theorems.- 8-Spaces of Constant Curvature.- 9-Variations of Energy.- 10-The Rauch Comparison Theorem.- 11-The Morse Index Theorem.- 12-The Fundamental Group of Manifolds of Negative Curvature.- 13-The Sphere Theorem.- References.
SynopsisRiemannian 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 background from readers, making it suitable for a wide variety of students and course structures. Its selection of topics has been deemed "superb" by teachers who have used the text. A significant feature of the book is its powerful and revealing structure, beginning simply with the definition of a differentiable manifold and ending with one of the most important results in Riemannian geometry, a proof of the Sphere Theorem. The text abounds with basic definitions and theorems, examples, applications, and numerous exercises to test the student's understanding and extend knowledge and insight intothe subject. Instructors and students alike will find the work to be a significant contribution to this highly applicable and stimulating subject., "This is one of the best (if even not just the best) book for those who want to get a good, smooth and quick, but yet thorough introduction to modern Riemannian geometry." ---Publicationes Mathematicae"In the reviewer's opinion, this is a superb book which makes learning a real pleasure." ---Revue Romaine de Mathematiques Pures et Appliquees"This main-stream presentation of differential geometry serves well for a course on Riemannian geometry, and it is complemented by many annotated exercises." ---Monatshefte F. Mathematik, 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 background from readers, making it suitable for a wide variety of students and course structures. Its selection of topics has been deemed "superb" by teachers who have used the text. A significant feature of the book is its powerful and revealing structure, beginning simply with the definition of a differentiable manifold and ending with one of the most important results in Riemannian geometry, a proof of the Sphere Theorem. The text abounds with basic definitions and theorems, examples, applications, and numerous exercises to test the student's understanding and extend knowledge and insight into the subject. Instructors and students alike will find the work to be a significant contribution to this highly applicable and stimulating subject.
LC Classification NumberQA641-670
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