Which Book on Riemannian Geometry Balances Intuition and Minimal Prerequisites?

In summary, the book "Relativity on curved manifolds" by de Felice and Clarke is a good book for someone looking for a math book on riemannian geometry that is not too formal. It covers the basics of differential geometry of curves and surfaces, and generalizes to R^n. The book is available on Amazon and is rated 4.5/5 stars.
  • #36
it is a very famous old book, with excellent content, but i have never heard it compared with the ones recommended here in terms of readability. but if you can read it, it will serve you well.
 
<h2> What is a good introductory book for differential geometry?</h2><p>A popular choice for an introductory book on differential geometry is "Differential Geometry of Curves and Surfaces" by Manfredo P. do Carmo. It covers the basics of curves and surfaces, as well as the fundamental concepts and theorems of differential geometry.</p><h2> Is there a book that focuses on applications of differential geometry?</h2><p>"Applied Differential Geometry" by William L. Burke is a well-regarded book that covers the applications of differential geometry in fields such as physics, engineering, and computer graphics.</p><h2> What is a good book for advanced topics in differential geometry?</h2><p>"Riemannian Geometry" by Manfredo P. do Carmo is a widely used book for advanced topics in differential geometry. It covers Riemannian manifolds, curvature, and other advanced concepts.</p><h2> Are there any books that use a more geometric approach to teaching differential geometry?</h2><p>"An Introduction to Differential Geometry" by T. J. Willmore is a highly recommended book for its geometric approach to teaching differential geometry. It also includes exercises and solutions for further practice.</p><h2> Is there a book that covers both differential and algebraic geometry?</h2><p>"Differential and Algebraic Geometry" by Jean Gallier is a comprehensive book that covers both differential and algebraic geometry, making it a great resource for those interested in both fields.</p>

FAQ: Which Book on Riemannian Geometry Balances Intuition and Minimal Prerequisites?

What is a good introductory book for differential geometry?

A popular choice for an introductory book on differential geometry is "Differential Geometry of Curves and Surfaces" by Manfredo P. do Carmo. It covers the basics of curves and surfaces, as well as the fundamental concepts and theorems of differential geometry.

Is there a book that focuses on applications of differential geometry?

"Applied Differential Geometry" by William L. Burke is a well-regarded book that covers the applications of differential geometry in fields such as physics, engineering, and computer graphics.

What is a good book for advanced topics in differential geometry?

"Riemannian Geometry" by Manfredo P. do Carmo is a widely used book for advanced topics in differential geometry. It covers Riemannian manifolds, curvature, and other advanced concepts.

Are there any books that use a more geometric approach to teaching differential geometry?

"An Introduction to Differential Geometry" by T. J. Willmore is a highly recommended book for its geometric approach to teaching differential geometry. It also includes exercises and solutions for further practice.

Is there a book that covers both differential and algebraic geometry?

"Differential and Algebraic Geometry" by Jean Gallier is a comprehensive book that covers both differential and algebraic geometry, making it a great resource for those interested in both fields.

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