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 determinetheir 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.
Exercises to the lecture Line Geometry.
The set of lines in 3-space is 4-dimensional. The first two parts of the lecturedeal 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.
Presentation of examples.
Homework (three times) .