Some hyperbolic plane models and hyperbolic Klingenberg plane classes

In this thesis, basic information about hyperbolic planes which are one of the important non-Euclidean planes, some information about hyperbolic plane models and some studies about Hyperbolic-Klingenberg planes which are constructed as a generalization of hyperbolic planes are presented briefly. Poincaré models which are the hyperbolic plane models obtained from the Euclidean plane, hyperbolic plane models of Sandler, the extension of the Sandler's model and the constructions of these models are given in detail in one chapter. In addition, some studies on projective subplanes and hyperbolic planes have been examined and the structure obtained by deleting all lines together with their points of projective non- Baer subplane from a finite projective plane has been introduced and the conditions under which remaining structure will indicate a hyperbolic plane have been given. Finally, results of Hyperbolic-Klingenberg models constructed by deleting a certain number m of equivalence classes of lines with their points from a finite Projective-Klingenberg plane are given.