Browsing by Author "Grundhöfer, Theo"

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    Fibrations of spheres by great spheres over division algebras and their differentiability
    (1990) Grundhöfer, Theo; Hähl, Hermann
    The authors answer the natural question: When is the fibration of S {2n-1} by great (n-1)-spheres determined by a division algebra differentiable? They show that this happens only for the classical Hopf fibrations, which are determined by the classical division algebras R, C, H and O.
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    Finite subunitals of the hermitian unitals
    (2022) Grundhöfer, Theo; Stroppel, Markus J.; Maldeghem, Hendrik van
    Every finite subunital of any generalized hermitian unital is itself a hermitian unital; the embedding is given by an embedding of quadratic field extensions. In particular, a generalized hermitian unital with a finite subunital is a hermitian one (i.e., it originates from a separable field extension).
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    Slanted symplectic quadrangles
    (1994) Grundhöfer, Theo; Joswig, Michael; Stroppel, Markus
    By "slanting" symplectic quadrangles W(F) over fields F, we obtain very simple examples of non-classical generalized quadrangles. We determine the collineation groups of these slanted quadrangles and their groups of projectivities. No slanted quadrangle is a topological quadrangle.
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    Unitals with many involutory translations
    (2023) Grundhöfer, Theo; Stroppel, Markus J.; Maldeghem, Hendrik van
    If every point of a unital is fixed by a non-trivial translation and at least one translation has order two then the unital is classical (i.e., hermitian).