Bernd,
maybe this what you are looking for:
reg = ParametricRegion[{{u v Cos[\[Theta]], u v Sin[\[Theta]], 1/2 (u^2 - v^2)},
0 < u < 1 && 0 < v < 1 && 0 < \[Theta] < 2 Pi}, {u, v, \[Theta]}];
RegionPlot3D[reg, Axes -> True, PlotPoints -> 30, ImageSize -> Large]
![enter image description here](https://community.wolfram.com//c/portal/getImageAttachment?filename=FlyingSoucer.png&userId=32203)
Regards to Austria -- Henrik