I am looking for a textbook(s) that discusses differential geometry, smooth manifolds etc. More precisely, I have been trying to find a textbook that covers the following topics:
- Differential geometry ( vector fields, forms, manifolds, mappings between manifolds, bundles, etc)
- Fibre bundle application to physics
- Lie theory and differential geometry
- Includes (or has some) illustrations
I am looking for something that is rigorous but not completely terse like a pure mathematics book, but also not so physical. I have found Marian's Fecko's book good however, the whole idea of working out and deriving definitions is not something I am particularly fond of. I have also read Isham's text and found myself needing to look up a lot of things to fill in the gaps.
