  The study of superfluid quantum vortices has long been an important area of
research, with previous work naturally focusing on two-dimensional and
three-dimensional systems, where rotation stabilises point vortices and line
vortices respectively. Interestingly, this physics generalises for a
hypothetical four-dimensional (4D) superfluid to include vortex planes, which
can have a much richer phenomenology. In this paper, we study the possibility
of skewed and curved vortex planes, which have no direct analogue in lower
dimensions. By analytically and numerically studying the 4D Gross-Pitaevskii
equation, we show that such vortex surfaces can be stabilised and favoured by
double rotation with unequal rotation frequencies. Our work raises open
questions for further research into the physics of these vortex surfaces and
suggests interesting future extensions to tilted vortex surfaces under
equal-frequency double rotation and to more realistic 4D models.
