Spreads admitting net generating regulizations

✍ Scribed by Rolf Riesinger

• Book ID: 104641935
• Publisher: Springer
• Year: 1996
• Tongue: English
• Weight: 981 KB
• Volume: 62
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00147806

✦ Synopsis

We say a spread S carries a regulization ~, if E is a collection of reguli contained in 8 and if each element of S, except at most two lines, is contained either in exactly one regulus of or in all reguli of E. Replacement of each regulus of P, by its complementary regulus (exceptional lines remain unchanged) yields the complementary congruence S~ of S with respect to Y;. If S~ is a hyperbolic or parabolic or elliptic linear congruence of lines, then Z is called a net generating, in particular, a hyperbolic or parabolic or elliptic regulization, respectively. For hyperbolic and parabolic regulizations we also give other geometric characterizations.