Abstract
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.
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Bickel, H. Stiffness in four-dimensional stable planes. Results. Math. 32, 47–60 (1997). https://doi.org/10.1007/BF03322523
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DOI: https://doi.org/10.1007/BF03322523