Riemannian Geometry

by Manfredo P. Do Carmo, Francis Flaherty (Translator)

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.

Genres: Mathematics, Science, Geometry, Textbooks, Reference

300 pages, Hardcover

First published January 1, 2008

About the author

Manfredo Perdigão do Carmo (15 August 1928, Maceió – 30 April 2018, Rio de Janeiro) was a Brazilian mathematician. He spent most of his career at IMPA and is seen as the doyen of differential geometry in Brazil.

Reviews

[Bogdan Suceava · Rating 5 out of 5]

The best introduction in the fundamental topics of Riemannian Geometry. This book helped me a lot. M. P. do Carmo accomplished a very useful construction that most probably will help several generations of mathematicians as they advance in this topic.

[Wissam Raji · Rating 5 out of 5]

I would say one of the best introductory books to Riemannian geometry with a nice simplification of treatment of the fundamental topics.

[Ella Novella · Rating 2 out of 5]

The cover image goes hard af and I want a tattoo of it. But oh my god was this a hard read starting from 0 knowledge of manifolds. Lesson learned: Start by learning the topology before tacking on a metric.