Riemannian Geometry: Theory & Applications
Sci Math Ref Econ Biz
About this book
"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 bea significant contribution to this highly applicable and stimulating subject."
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.