Riemannian Geometry /
Manfredo Perdigão do Carmo ; translated by Francis Flaherty.
- Boston : Birkhauser, c1992.
- 300 p. : ill. ; 25 cm.
Translation of the 2nd ed. of: Geometria riemanniana.
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.