Riemannian Geometry: Theory & Applications (Mathematics: Theory & Applications)
Product ID: 52329979
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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 intothe subject. Instructors and students alike will find the work to be a significant contribution to this highly applicable and stimulating subject. Review: A well written text! - Riemannian geometry was the first topic I considered 'difficult' when I was at university. I didn't study it at undergraduate level but needed a background in riemannian geometry for a Master's level module on Morse Theory. So I essentially had to teach myself Riemannian geometry. I used Do Carmo's Differential Geometry of Curves and Surfaces at undergraduate level: I found it very long-winded, dry and seemed very much proof and proof and proof which gave the text a disconnected feel and quite painful to follow after a while. But it's counterpart, this text, I found much easier to follow for independent study. It's probably the best text on the subject but it does lack diagrams and the explanations of concepts are often quite brief. This text does have some excellent problems for you to attempt, but there are no solutions and there should be, that is my main complaint about the text. So in summary, a bit more detailed explanation and a lot more diagrams to support these details would massively improve the text. If you're studying this topic at university then this book is ideal as you'll have all the explanation in lectures and this text will serve as very concisely written mathematics. Review: Un clásico imprescindible. - Este libro es la traducción en los primeros setenta de un texto en portugués. Su principal interés reside en el hincapié que hace en destacar el papel que juegan las distintas hipótesis y condiciones en los teoremas de la geometria diferencial. Si alguien quiere entender lo que está haciendo al manipular símbolos este es el libro.
| Best Sellers Rank | 300,594 in Books ( See Top 100 in Books ) 13,244 in Scientific, Technical & Medical |
| Customer Reviews | 4.7 out of 5 stars 91 Reviews |
J**E
A well written text!
Riemannian geometry was the first topic I considered 'difficult' when I was at university. I didn't study it at undergraduate level but needed a background in riemannian geometry for a Master's level module on Morse Theory. So I essentially had to teach myself Riemannian geometry. I used Do Carmo's Differential Geometry of Curves and Surfaces at undergraduate level: I found it very long-winded, dry and seemed very much proof and proof and proof which gave the text a disconnected feel and quite painful to follow after a while. But it's counterpart, this text, I found much easier to follow for independent study. It's probably the best text on the subject but it does lack diagrams and the explanations of concepts are often quite brief. This text does have some excellent problems for you to attempt, but there are no solutions and there should be, that is my main complaint about the text. So in summary, a bit more detailed explanation and a lot more diagrams to support these details would massively improve the text. If you're studying this topic at university then this book is ideal as you'll have all the explanation in lectures and this text will serve as very concisely written mathematics.
E**O
Un clásico imprescindible.
Este libro es la traducción en los primeros setenta de un texto en portugués. Su principal interés reside en el hincapié que hace en destacar el papel que juegan las distintas hipótesis y condiciones en los teoremas de la geometria diferencial. Si alguien quiere entender lo que está haciendo al manipular símbolos este es el libro.
M**N
Gut
Habe es für mein Studium gebraucht und fand es sehr hilfreich. Hat mein Verständnis erweitert, die VL unterstützt. Wer sich deutsche Mathebücher kaufen will, sollte sich endlich daran gewöhnen, dass die wirklichen Referenzen auf Englisch sind. Dieses Buch ist so eine Referenz. Klare Empfehlung, darf in keinem Bücherregal fehlen.
M**H
Important book
Interesting and important book
R**E
Buon servizio
Puntuale, come da descrizione
F**A
Excelent introduction
Do Carmo's book it's a sucessfully introduction to Riemannian geometry, Un my personal point oficina view it gives a general Outlook about this subject so people who doesn't know anything about Riemannian geometry I recommend this book to introduce un this awesome wolrd of geometry with a previous good calculs Andrea linear algebra knowledge.
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