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Normisomorphismen und Normkurven endlichdimensionaler projektiver Desargues-Räume

Normal isomorphisms and normal curves in finite-dimensional desarguesian projective spaces

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Abstract

In a finite dimensional desarguesian projective space the set of all points of intersection of homologous lines of two projective bundles of lines is called a non-degenerated (n. d.) normal curve, if the projective isomorphism is nondegenerated. Every frame determines a n. d. projective isomorphism of two bundles of lines called a normal isomorphism; every n. d. projective isomorphism of two bundles of lines is a normal isomorphism. A definition of osculating subspaces of a normal isomorphism is given and we show how the osculating subspaces can be constructed by using linear mappings. Simple examples show that there may be collineations fixing a n. d. normal curve but not fixing the osculating subspaces of the associated normal isomorphism. The set of osculating hyperplanes of a normal isomorphism is a n. d. normal curve in the dual space if and only if a certain number-theoretical condition holds.

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Authors and Affiliations

  1. Institut für Geometrie, Technische Universität, Gußhausstraße 27-29, A-1040, Wien, Österreich

    Hans Havlicek

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  1. Hans Havlicek
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Herrn emer.O. Univ.-Prof. Dr. J. Krames zum 85. Geburtstag gewidmet

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Havlicek, H. Normisomorphismen und Normkurven endlichdimensionaler projektiver Desargues-Räume. Monatshefte für Mathematik 95, 203–218 (1983). https://doi.org/10.1007/BF01351998

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  • DOI: https://doi.org/10.1007/BF01351998

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