Best books for Differential Geometry?

majutsu

Thanks everyone for great suggestions and ideas. I am still reading . . . :) I actually got detoured, because I wanted to brush up PDE and the fine points of advanced calculus before DG, so that's where I'm at the last 2 months or so.

mathwonk

here is another free book, without tensor machinery.

last topic on this webpage.

http://www.math.uga.edu/~shifrin/

uni

Hi,
Mechanics in differential geometry by Yves Talpaert (Springer) is a comprehensive and very useful book, both in differential geometry and physics.
Greg

ziggy

i'm a third year math student and the best one i've come across is 'differential geometry, schaum's outline series, auther-martin lipschultz'. hope this is helpfull.

Ruslan_Sharipov

My geocities.com/r-sharipov site is now off. Use the following two sites for my books:

http://ruslan-sharipov.ucoz.com
http://freetextbooks.narod.ru

wofsy

For beginning geometry there are two truly wonderful books, Barrett O'neill's Elementary Differential Geometry and Singer and Thorpe's Lecture Notes on Elementary Topology and Geometry. Singer and Thorpe are well known mathematicians and wrote this book for undergraduates to introduce them to geometry from the modern view point. The book has wonderful explanations and uses the modern theory of connections. Plus it covers calculus on manifolds, De Rham's Theorem and some essential topology such as the theory of covering spaces.

I do not recommend Hicks's book. It is not intuitive and much of the material is just thrown at you. The center of differential geometry is the theory of connections. Hick's treament I found unreadable. If anything use it as a reference. Spivak's book is probably great but it is big.

If you want to learn diff geo for physics then read a book on General Relativity but not Wald. That book is tough and non-intuitive. Try A first course in GR by Schutz.

pamparana

Just started with Elementary Differential Geometry by Andrew Pressley and the book seems great for self-study.

zhentil

The books I started with: John Lee's Smooth Manifolds, Boothby, Spivak's Calculus on Manifolds
The books I reach for now: Hirsch's Differential Topology, Kobayashi and Nomizu

The advice I'd offer the newcomer is to steer well clear of "easy" intros to differential geometry. Dependence on coordinate systems especially is a habit you'd rather never develop.