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.
DownloadA 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.
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