Abstract.
We generalize a result of Kramer, see [7, 10.7 and 10.10], on generalized quadrangles associated with isoparametric hypersurfaces of Clifford type to Tits buildings of type C2 derived from arbitrary isoparametric hypersurfaces with four distinct principal curvatures in spheres: two distinct points p and q of a generalized quadrangle associated with an isoparametric hypersurface in the unit sphere of a Euclidean vector space can be joined by a line K if and only if (p − q)/||p − q|| is a line. This line is orthogonal to K. Dually, two distinct lines L and K intersect if and only if (L − K)/||L − K|| is point.
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Received: 14 October 2005
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Immervoll, S. A note on isoparametric generalized quadrangles. Arch. Math. 87, 478–480 (2006). https://doi.org/10.1007/s00013-006-1758-y
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DOI: https://doi.org/10.1007/s00013-006-1758-y