On Some Finite Hyperbolic Spaces

Abstract

Let pi be a finite projective plane of order n. Consider the substructure pi(n+2) obtained from pi by removing n + 2 lines (including all points on them) no three are concurrent. In this paper, firstly, it is shown that pi(n+2) is a B - L plane and it is also homogeneous. Let PG(3, n) be a finite projective 3-space of order n. The substructure obtained from PG(3, n) by removing a tetrahedron that is four planes of PG(3, n) no three of them are collinear is a finite hyperbolic 3-space (Olgun-Ozgar [10]). Finally, we prove that any two hyperbolic planes with same parameters are isomorphic in this hyperbolic 3-space. These results are appeared in the second author's Msc thesis.