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The study of superfluid quantum vortices has long been an important area ofresearch, with previous work naturally focusing on two-dimensional andthree-dimensional systems, where rotation stabilises point vortices and linevortices respectively. Interestingly, this physics generalises for ahypothetical four-dimensional (4D) superfluid to include vortex planes, whichcan have a much richer phenomenology. In this paper, we study the possibilityof skewed and curved vortex planes, which have no direct analogue in lowerdimensions. By analytically and numerically studying the 4D Gross-Pitaevskiiequation, we show that such vortex surfaces can be stabilised and favoured bydouble rotation with unequal rotation frequencies. Our work raises openquestions for further research into the physics of these vortex surfaces andsuggests interesting future extensions to tilted vortex surfaces underequal-frequency double rotation and to more realistic 4D models.

Curved vortex surfaces in four-dimensional superfluids: I. Unequal-frequency double rotations