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Connected 4-dimensional stable planes with many central collineations

✍ Scribed by Hans-Peter Seidel

Publisher: Springer
Year: 1990
Tongue: English
Weight: 753 KB
Volume: 36
Category: Article
ISSN: 0046-5755
DOI: 10.1007/bf00150802

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✦ Synopsis

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 4dimensional generalized symmetric planes yields the desired classification.

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4-dimensional compact projective planes with a 7-dimensional collineation group

✍ Dieter Betten 📂 Article 📅 1990 🏛 Springer 🌐 English ⚖ 959 KB

The classification of 4-dimensional compact projective planes having a 7-dimensional collineation group is completed. Besides one single shift plane all such planes are either translation planes or dual translation planes.