After successful completion of the course, students are able to handle torsal and
developable ruled surfaces in an analytic and constructive way and are able to determine
their invariants. Students know the principal properties of line congruences,
in detail their envelopes and their developable surfaces.
Projective Geometry will help to get a deeper understanding of the structure of the
set of lines in 3-space.

The set of lines in 3-space is 4-dimensional. The first two parts of the lecture
deal with Euclidean geometry of
*) ruled surfaces (1-dim sets of lines) and
*) line congruences (2-dim sets of lines).

A third part shall present projective geometry of the set of lines in 3-space.
The point model of this set is a quadric in 5-space that is used for many investigations.

Lecture with examplpes.

Oral exam.

Computational Line Geometry by H. Pottmann, J. Wallner Springer, 2001

Liniengeometrie, J. Hoschek, BI-Taschenbuch, Zürich 1971.