Abstract
This paper gives a complete classification of all connected 4-dimensional stable planes with the property that every point is the centre of a non-trivial central collineation. It is shown that under these assumptions the automorphism group has an open orbit on the point space. This implies the existence of an open subplane that carries the additional structure of a generalized symmetric space in the sense of differential geometry. Now the classification of all 4-dimensional generalized symmetric planes yields the desired classification.
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Dedicated to Professor H. Salzmann on his 60th birthday
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Seidel, HP. Connected 4-dimensional stable planes with many central collineations. Geom Dedicata 36, 375–388 (1990). https://doi.org/10.1007/BF00150802
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DOI: https://doi.org/10.1007/BF00150802