I can figure out how to do a rigid rotation in n dimensions. Next I want to look at non-rigid rotations. Lets says that we have a rotation sphere of fluid in 3D. How mathematically does that rotate? It is important how viscous the fluid is. If it is infinite viscous them it would essentially be a solid, right? So it seems that there could be a single expression with a viscosity term. A fluid sphere with zero viscosity would be a superfluid, I think, and hence excluded. Or perhaps not.