I would like to get reccomendations for a text on "advanced" vector analysis. By "advanced", I mean that the discussion should take place in the context of Riemannian manifolds and should provide coordinate-free definitions of divergence, curl, etc. I would like something that has rigorous theory but also plenty of concrete examples and a mixture of theoretic/concrete exercises.
The text that I have seen that comes closest to what I'm looking for is Janich's Vector Analysis. The Hatcheresque style of writing in this particular text though isn't really suitable for me.
Looking forward to your reccomendations, thanks.