Literature on differential geometry, suggestions?

  • #1
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?
 

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  • #2
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Try "Riemannian Manifolds: An Introduction to Curvature" by John M. Lee.
 
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  • #3
thanks, any other suggestions?
 
  • #4
robphy
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ONeill's Semi-Riemannian Geometry
 

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