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Partitions of Three-Dimensional Pappian Projective Spaces by Ovoidal Quadrics

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Abstract

In his article Partitioning Projective Geometries Into Caps, Ebert showed inter alia that every finite three-dimensional projective space can be partitioned by ovoidal quadrics. The aim of the present note is to generalize this result by identifying a more comprehensive class of three-dimensional projective spaces which admit partitions of this kind. In addition, the group of all collineations which preserve such a partition is determined.

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References

  1. Ebert, G. L.: Partitioning projective geometries into caps, Canad. J.Math. 37 (1985), 1163– 1175.

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  2. Hughes, D. R. and Piper, F. C.: Projective Planes, Springer, New York, Heidelberg, Berlin, 1973.

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Authors and Affiliations

  1. Department of Pure and Applied Mathematics, University of Namibia, Private Bag, 13301, Windhoek, Namibia

    Günter Heimbeck

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  1. Günter Heimbeck
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Heimbeck, G. Partitions of Three-Dimensional Pappian Projective Spaces by Ovoidal Quadrics. Geometriae Dedicata 71, 119–127 (1998). https://doi.org/10.1023/A:1005051128752

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  • DOI: https://doi.org/10.1023/A:1005051128752

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