Let $a,b,c\in\mathbb{R}^3$ with $a\wedge b\wedge c\ne 0$ and $a^2>b^2$.
What is the form of this equation $p(\theta,t)=e^{a\wedge c\theta}(a+be^{a\wedge bt})e^{-a\wedge c\theta}$ in standard vector coordinates, where $\theta,t\in\mathbb{R}$.
I am not really sure at all how to go about converting it. I have read some basics on rotors, but cannot find anything on expressions involving exponentials as rotors.
My ultimate goal is to examine the features of this surface; i.e. whether or not it is compact or regular.