Riemannian Geometry (Mathematics: Theory and Applications) - Hardcover

Carmo, Manfredo P.Do; Do Carmo, M.P.

Hardcover

ISBN 10: 3764334908 ISBN 13: 9783764334901

Publisher: Birkhauser Verlag AG, 1991

Synopsis

This is a new and expanded edition of this textbook for first-year graduate students in mathematics and physics, discussing the basic language of Riemannian geometry and presenting some of its most fundamental theorems. It is elementary in that it only assumes a modest background from the readers, making it suitable for a wide variety of students and course structures. It features basic definitions and theorems, examples and numerous exercises. The book begins with the definition of a differential manifold and ends with one of the most important results in Riemmanian geometry - a proof of the Sphere Theorem.

About this title

Review

"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"

"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

Edition details

• Publisher: Birkhauser Verlag AG
• Publication date: 1991
• Language: English
• ISBN 10: 3764334908
• ISBN 13: 9783764334901
• Binding: Hardcover
• Edition number: 4
• Number of pages: 300