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

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!