Clairaut’s theorem in Minkowski space. (English) Zbl 1295.53009

Summary: We consider some aspects of the geometry of surfaces of revolution in three-dimensional Minkowski space. First, we show that Clairaut’s theorem, which gives a well-known characterization of geodesics on a surface of revolution in Euclidean space, has an analogous result in three-dimensional Minkowski space. We then illustrate the significant differences between the two cases which arise in spite of their formal similarity.


53A35 Non-Euclidean differential geometry
53A05 Surfaces in Euclidean and related spaces