Stiffness in four-dimensional stable planes

We present stiffness results for four-dimensional stable planes showing that a non-projective plane is suffer than a projective one. Whereas the best possible result in projective planes is that the isotropy group of a non-degenerate quadrangle has order at most two, we obtain that certain degenerate quadrangles with two non-compact sides have a zero-dimensional isotropy group. In [2] our stiffness results help to determine all four-dimensional stable planes with an at least nine-dimensional automorphism group. Our results improve those of Löwen [12], 5.2. We introduce the Freudenthal compactification as a new tool.