This is just a reference request. Does anybody has or know a book with a short handed formulary for Calculus on Manifold. I could do it, but surely someone already have done it better than I would.
It should at least have: Definition of Hodge Dual, Exterior Differentiation, Lie Derivatives, Interior Derivative, Cartan Structure Equation, etc...
If you don't have any reference, could you at least tell me which formulas do you think would be useful to put in it? Thanks
Gadea et al's book Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers has a 56-page long appendix (Chapter 7) listing formulas used in smooth manifold theory. It probably has everything you are looking for, and more.