Differential Geometry book on 3D Euclidn space - worth reading?

[quantum_smile]

I bought a book (Differential Geometry by Kreyszig) based on really good reviews because I'm planning to learn general relativity later. I guess I didn't pay enough attention to the description because apparently it's completely focused on "three-dimensional Euclidean space."

Will this book even be worth reading even though it's so limited to Euclidean space? If not, could someone recommend another a differential geometry book that may have solutions available (so that it's okay for self-study)?

 

[jedishrfu]

The classic book on GR: Gravitation by Misner, Thorne and Wheeler covers tensor analysis, differential forms in the context of 4D differerntial geometry.

Another really good book is Einstein Gravity in a Nutshell by Zee which is fairly recent and covers a lot of new material not in Wheelers book.

I think Kreyszigs book will still be useful though because we still think in 3D to understand the concepts before we extend them to other dimensions.

 

[mathwonk]

from my reading of the books contents, it is rather focused entirely on differential geometry of curves and surfaces, which I think is quite basic and central to understanding the subject.

 

[quantum_smile]

Okay, awesome. I guess I'll get to work on it. Thanks!

 

[Daverz]

As well as being a fun subject on its own, studying the "Differential Geometry of Curves and Surfaces" should give you some intuition about curvature.

If you want a book that also covers local surface theory but then ramps up to some pretty sophisticated math (fiber bundles and gauge theory), but without a background in topology needed, there's the book by Darling:

https://www.amazon.com/dp/0521468000/?tag=pfamazon01-20