On the hyperbolic Klingenberg plane classes constructed by deleting subplanes

Abstract

In this study we investigate the structures constructed by deleting a subplane from a projective Klingenberg plane. If the superplane and the subplane are infinite, then it can be easily seen that the remaining structure satisfies the conditions of a hyperbolic Klingenberg plane. In this study we show that the remaining structure is the hyperbolic Klingenberg plane if the inequality r >= m(2) + m + 1 + root m(2) + m + 2 holds when the superplane and the subplane are finite and t, r and t, m are their parameters, respectively.