I am trying to teach myself differential geometry using Lee's Introduction to Smooth Manifolds.
To test my understanding, and learn the subject better, I am looking for a good problem book in differential geometry.
The kind of problems I am looking for are non-computational ones. The problems which are very much like theorems in themselves.
The best I can describe the kind of book I am looking for is something like Berkeley's Problems in Mathematics is for undergraduate mathematics.
The problems are not too hard. But each problem teaches something nice.
Try this new arrival:
Springer Link
Smooth Manifolds Authors: Rajnikant Sinha
ISBN: 978-81-322-2103-6 (Print) 978-81-322-2104-3 (Online)