Minding's isometries of ruled surfaces in Galilean and pseudo-Galilean space
by
Blaženka Divjak
Faculty of organization and informatics, University of Zagreb, Croatia

The Galilean and pseudo-Galilean geometry are the real Cayley-Klein geometries (of projective signature (0, 0, +, +) and (0, 0, +, -)).The absolute of the Galilean (pseudo-Galilean geometry) is an ordered triple { \omega, f, I} where \omega is the ideal (absolute) plane, f line in \omega and I is the fixed elliptic (hyperbolic) involution of the points of f.

There are three types of regular ruled surfaces in pseudo-Galilean space G₃¹ similarly to the Galillean case G₃¹. For any such surface a ''Drall'' and an associated triheadron are determined. In the same way as in the theory of curves in G₃ and G₃¹ the curvature and torsion for each type can be defined and associated derivative equations obtained.

Minding isometry is such isometric transformation between ruled surfaces \Phi and \Phi ^* that transforms the direction field of \Phi to direction field of \Phi ^* . The Minding isometries of all three types of ruled surfaces in G₃ and G₃¹ are described.

Abstract

Date received: March 10, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadz-51.