Normisomorphismen und Normkurven endlichdimensionaler projektiver Desargues-R�ume

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.