SUBJECT
Title
Geometry III
Type of instruction
lecture + practical
Level
master
Faculty
Part of degree program
Recommended in
Semesters 1-4
Typically offered in
Autumn/Spring semester
Course description
Projective geometry: projective space over a field, projective subspaces, dual space, collineations, the Fundamental Theorem of Projective Geometry. Cross ratio. The theorems of Pappus and Desargues, and their rôle in the axiomatic foundations of projective geometry. Quadrics: polarity, projective classification, conic sections.
Hyperbolic geometry: Minkowski spacetime, the hyperboloid model, the Cayley-Klein model, the conformal models of Poincaré. The absolute notion of parallelism, cycles, hyperbolic trigonometry.
Readings
M. Berger: Geometry I–II (Translated from the French by M. Cole and S. Levy).Universitext, Springer–Verlag, Berlin, 1987.