Textbooks on differential geometry

Kobiyashi and Nomizu, Foundations of Differential Geometry, vol. I & II has it all. Not an easy read. Best of luck with it.

Doesn't have much on physics, though. For that you might try Hawking and Ellis, Large Scale Structure of Space-Time; lots of Riemannian geometry from the ground up and applied to General Relativity. Also not an easy read. And yes, it is the Hawking.

These works might be available online, perhaps even legitimately so.

Tags:

Riemannian Geometry

Differential Geometry

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