This book is a good text connecting differential forms and the Gauss-Bonnet Theorem (which match my project topic). But this book is too compact for me to self-study. Is there any alternative to this book, which, in the same way, introduce differential forms and then prove the Stoke's theorem and the Gauss-Bonnet Theorem using Cartan structural equations from differential forms?
2026-03-31 16:53:18.1774975998
Alternative book to do Carmo Differential forms and Applications
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If you aren't ready to read some graduate texts in differential geometry (of which there are plenty, but it's hard to find texts that do things just with differential forms), I recommend this book by Jeanne Clelland
https://bookstore.ams.org/gsm-178/.
You haven't told us your background in analysis, topology, etc.
For lectures by a master, see Chern/Chen/Lam's book:
https://www.worldscientific.com/worldscibooks/10.1142/3812