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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 [InlineEquation not available: see fulltext.] holds when the superplane and the subplane are finite and t, r and t, m are their parameters, respectively. MSC: 51D20, 05B25. [ABSTRACT FROM AUTHOR]

In this paper we study Moufang-Klingenberg planes M(A) defined over a local alternative ring A of dual numbers. We show that some collineations of M(A) preserve cross-ratio and thus establish a relation between harmonicity and harmonic position. [ABSTRACT FROM AUTHOR]