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Higher dimensional analogues of Klein's quadric

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Abstract

The basic idea is a mapping from d-dimensional subspaces of a 2d-dimensional vector space onto points in a projective space of dimension \(\left( \begin{gathered} 2d \hfill \\ d \hfill \\ \end{gathered} \right) - 1\). We develop conditions under which a point in the larger projective space is an image point under this mapping. We also develop conditions corresponding to cases where the d-dimensional vector spaces do or do not intersect.

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References

  1. Mason, G. and Shult, E. E., ‘The Klein correspondence and the ubiquity of certain translation planes’, Geom. Dedicata 21 (1986), 29–50.

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  2. Veblen, O. and Young, J. W., Projective Geometry, Vol. I, Blaisdell Publishing Company, New York, 1938.

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Authors and Affiliations

  1. Dept. of Pure and Applied Mathematics, Washington State University, 99164-3113, Pullman, WA, U.S.A.

    T. G. Ostrom

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  1. T. G. Ostrom
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Dedicated to A. Wagner on his 60th birthday

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Ostrom, T.G. Higher dimensional analogues of Klein's quadric. Geom Dedicata 41, 207–217 (1992). https://doi.org/10.1007/BF00182421

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  • DOI: https://doi.org/10.1007/BF00182421

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