Riemannian Geometry written by Manfredo P.Do Carmo, M.P. do Carmo , Francis Flaherty
It is a new and expanded version of this textbook for first-12 months graduate students in mathematics and physics, discussing the essential language of Riemannian geometry and presenting a few of its most elementary 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 guide begins with the definition of a differential manifold and ends with one of the most necessary ends in Riemmanian geometry – a proof of the Sphere Theorem.
I have gone by means of many books about riemannian geometry, only to seek out that most of them are enjoying magic in entrance of me. In relation to curvature and variation of power (arc length), a lot of the guide are just playing around with the notations with out drawing any geometric insight. When defining Levi-Civita connections, many books simply list out four meaningless formulae. I was so completely satisfied to learn this book because it explains every part in riemannian geometry in a clear and concise way. Theoretical details and geometrical interpretations are each having their place on this book.
Just one thing to notice: This book is a basic elementary introductory text in riemannian geometry. Those who need to know more ought to seek the advice of different book. But, as a first e-book in riemannian geometry, this guide is undoubtedly the best.
I had the pleasure of taking a course in Riemannian Geometry from the writer himself, utilizing the Portuguese version of this book. Do Carmo managed to cover the entire thing in a single semester without breaking a sweat; I don’t understand how he managed, or how we did. The fact is that the book is extremely well-written. It gives geometric insight but does not avoid computations. Additionally, the choice of topics is great, and they’re ordered in a approach that enhances the logical unity of the whole. The English translation appears to be every bit pretty much as good as the original. For a first course in Riemannian Geometry, this ebook might make a geometer out of you.