Criteria for two-dimensional circle planes
We give some easy to use criteria for deciding whether a Möbius plane, Laguerre plane or Minkowski plane, given in some normal form, is 2-dimensional. As an application of our results we prove that a Laguerre plane or Minkowski plane with a given topology on the point set is a (topological) 2-dimensional plane if and only if each derived affine plane at points of at least one parallel class is 2-dimensional with respect to the induced topology.
SubjectsField of Research::01 - Mathematical Sciences::0101 - Pure Mathematics::010102 - Algebraic and Differential Geometry
- Engineering: Reports