ON SOME FINITE HYPERBOLIC SPACES

Olgun S., SALTAN M.

ARS COMBINATORIA, vol.107, pp.317-324, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 107
  • Publication Date: 2012
  • Journal Name: ARS COMBINATORIA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.317-324
  • Anadolu University Affiliated: Yes

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.