Abstract
A complete overview of all orthogonality-preserving Plücker transformations in finite dimensional hyperbolic spaces with dimension other than three is given. In the Cayley-Klein model of such a hyperbolic space all Plücker transformations are induced by collineations of the ambient projective space.
Similar content being viewed by others
References
H. Brauner,Geometrie projektiver Räume I. B. I. Wissenschaftsverlag, Mannheim-Wien-Zürich, 1976.
—,Geometrie projektiver Räume II. B. I. Wissenschaftsverlag, Mannheim-Wien-Zürich, 1976.
W. Benz,Geometrische Transformationen. B. I. Wissenschaftsverlag, Mannheim-Leipzig-Zürich, 1992.
W. Benz andE. M. Schröder, Bestimmung der orthogonalitätstreuen Permutationen euklidischer Räume.Geom. Dedicata 21 (1986), 265–276.
W. L. Chow, On the geometry of algebraic homogeneous spaces.Ann. of Math. 50 (1949), 32–67.
R. Frank, Ein lokaler Fundamentalsatz für Projektionen.Geometriae Dedicata 44 (1992), 53–66.
H.-R. Friedlein, Normalformen für Bewegungen in hyperbolischen Räumen.J. Geom. 23 (1984), 61–71.
O. Giering,Vorlesungen über höhere Geometrie. Vieweg, Braunschweig-Wiesbaden, 1982.
S. Gudder, Metric Spaces over ordered Fields.Demonstr. Math. 19, No. 1 (1996), 165–183.
H. Havlicek, On Plücker Transformations of generalized elliptic spaces.Rend. Mat. Appl., VII Ser.14 (1994), 39–56.
—, Symplectic Plücker Transformations.Math. Pannonica 6 (1995), 145–153.
R. Höfer, Kennzeichnungen hyperbolischer Bewegungen durch Lineationen.J. Geom. 61 (1998), 56–61.
W.-L. Huang, Adjacency Preserving Transformations of Grassmann Spaces.Abh. Math. Sem. Univ. Hamburg (in print).
J.-H. Kroll andK. Sörensen, Hyperbolische Räume.J. Geom. 61 (1998), 141–149.
J. Lester, On Distance Preserving Transformations of Lines in Euclidean Three-Space.Aequat. Math. 18 (1985), 69–72.
H. Lenz,Vorlesungen über projektive Geometrie. Akademische Verlagsgesellschaft Geest & Portig K.-G., Leipzig, 1965.
W. Więsław,Topological Fields. Marcel Dekker, Inc., New York-Basel, 1988.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
List, K. On orthogonality-preserving plücker transformations of hyperbolic spaces. Abh.Math.Semin.Univ.Hambg. 70, 63–75 (2000). https://doi.org/10.1007/BF02940902
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02940902