Literature on differential geometry, suggestions?

[saminator910]

I am reading Spivak, Calculus on manifolds, and I have a basic working knowledge of topology through Mendelson, "Introduction to Topology", I want to learn more about differential geometry, especially co variant derivatives, levi-civita connections, Ricci and Rieman curvature tensors. I know about the fundamental forms, and Rieman metrics. I am interested in general relativity but It's impossible for me to learn anything substantial about it without learning more about differential geometry. By the way, I am very familiar with differential forms, differentiable manifolds, and the classic multivariable stuff. Any suggestions?

 

[yenchin]

Try "Riemannian Manifolds: An Introduction to Curvature" by John M. Lee.

 

[saminator910]

thanks, any other suggestions?

 

[robphy]

ONeill's Semi-Riemannian Geometry