I was wondering if it is possible to define the exterior derivative of a quaternionic valued function. I am doing the quaternionic analogue of a previously complex valued computation, namely something like $\omega = \frac{h}{\sqrt{1+|h|^2}}$ where $h$ is a quaternionic variable and I would like to compute $d\omega$.
Is this possible to do over $H$? In the complex case I treated $z$ and $\bar{z}$ as independent variables and computed using $\omega = \frac{z}{\sqrt{1+|z|^2}}$, with $d\omega$ being in terms of $dz$ and $d\bar{z}$.