TY - BOOK AU - Carmo,Manfredo Perdigao do TI - Riemannian Geometry SN - 0817634908 (acidfree) AV - QA649 .C2913 1992 U1 - 516.3/73 20 PY - 1992/// CY - Boston PB - Birkhauser KW - Geometry, Riemannian N1 - Translation of the 2nd ed. of: Geometria riemanniana N2 - 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 ER -