A collection of cheatsheest regarding the basic differential object on Smooth Manifolds and all the formulae relating them.
The plan is to realize a comprehensive collection of basic algebraic relation in differential geometry.
As always... Contributors are welcome!
https://www.overleaf.com/read/fjxqcdvyqnwt
Since the early days of Differential Geometry the importance of formulae that relate various differential objects on a manifold has been apparent. Let us mention among others the Bianchi identities, Weitzenb¨ock formulae, and Fr¨olicher-Nijenhuis calculus. It should be noted that all the above results can be obtained by elementary, although tedious and long, computations. Their importance lies in the psychological and practical plane, as they permit to work with the quantities in question without undergoing error-prone calculations, thus forming a swiss-knife kit of a differential geometer.
- Dedicated sty file including macros for the operator
- Setup Overleaf Project (https://www.overleaf.com/help/230-how-do-i-push-a-new-project-to-overleaf-via-git#.WyQAJKczb6Q)
- Table including covariant derivative and hodge operators
- Generalization of contraction and Lie to Multivector
- Further generalization to section of Lie algebroid ( pag 20, 21 https://arxiv.org/abs/math/0401221)
- Fields constitute a lie algebra. Lie algebras determine a chain complex (Eilenberg-Chevalley). -> Relation of generalized operator with EC boundary operator
- comprehensive bibliography in bibtex