Rigid circular string in four spatial dimensions ($X=A(t)\cos \sigma +B(t)\sin \sigma$)

If $A(t)$ and $B(t)$ are perpendicular four-dimensional spatial vectors of equal fixed magnitude, every constant-time slice is a planar circle. Opposite rotations in two orthogonal coordinate planes can produce a Nambu–Goto action solution with constant radius and a rotating plane. The induced worldsheet metric can be constant even though the embedding moves. Rotating Cartesian axes clarify its shape without removing its kinetic target-space energy.