A diffeomorphism is a type of isomorphism between smooth manifolds. It is defined as a function. The rules are as follows:

- The function must be continuously differentiable - Its inverse must also be continuously differentiable - It must be a bijection (one-to-one) between points

There are also harmonic diffeomorphisms (HARMONIC DIFFEOMORPHISMS OF MANIFOLDS, E. Stepanov). Whereas its partial derivatives sum to zero, and its laplacian is also zero.