  As is well-known, two-dimensional and three-dimensional superfluids under
rotation can support topological excitations such as quantized point vortices
and line vortices respectively. Recently, we have studied how, in a
hypothetical four-dimensional (4D) superfluid, such excitations can be
generalised to vortex planes and surfaces. In this paper, we continue our
analysis of skewed and curved vortex surfaces based on the 4D Gross-Pitaevskii
equation, and show that certain types of such states can be stabilised by
equal-frequency double rotations for suitable parameters. This work extends the
rich phenomenology of vortex surfaces in 4D, and raises interesting questions
about vortex reconnections and the competition between various vortex
structures which have no direct analogue in lower dimensions.
