Any recommendations for a Differential Geometry book?

[qspeechc]

Hi everyone.

I am a senior undergrad math major and I'm looking for a Differential Geometry book to self-study. I have studied most/all of the other undergrad topics: algebra; real and complex analysis; point-set topology; etc.
Any recommendations? Thanks

 

[Quantumjump]

whatever book you try, make sure it cover the manifold approach, since its the very heart of geo-diff

 

[Daverz]

Elements of Differential Geometry by Millman & Parker. Covers the usual local and global theories of curves and surfaces as well as manifolds.

 

[qspeechc]

Ok, thanks Daverz. Dr Carlson's review on amazon.com has convinced me to get this book. Can you recommend a book to follow this one?

 

[Daverz]

Ok, thanks Daverz. Dr Carlson's review on amazon.com has convinced me to get this book. Can you recommend a book to follow this one?

Differential Forms and Connections by R. W. R. Darling
Differential Geometry: Curves - Surfaces - Manifolds by Kühnel
Riemannian Geometry by do Carmo

Or you could go more in the direction of manifolds, topology, or differential equations.

 

[Fredrik]

Introduction to smooth manifolds, by John M. Lee. And Riemannian manifolds: an introduction to curvature, by the same author. Both are excellent. The latter covers connections, covariant derivative, parallel transport and curvature. The former covers everything else: Manifolds, tensor fields, Lie groups, differential forms, integration on manifolds, etc.

 

[qspeechc]

Thank-you Daverz and Fredrik. Looks like I have plenty of reading!