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Cheatsheets on the formulae relating differentiantial operator on Smooth Manifolds.

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Differential-Geometer-Toolbox

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!

Overleaf Version

https://www.overleaf.com/read/fjxqcdvyqnwt

The swiss army knife for differential geometers

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.

-- https://arxiv.org/abs/1503.08740

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Cheatsheets on the formulae relating differentiantial operator on Smooth Manifolds.

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