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.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 ...
|Author||:||Manfredo P. do Carmo|
|Publisher||:||Springer Science & Business Media - 1992|