On The Embedding of Complements of Some Hyperbolic Planes

Abstract

In this paper, we studied that a linear space, which is the complement of a linear space having points are not on a trilateral or a quadrilateral in a projective subplane of order $m$, is embeddable in a unique way in a projective plane of order $n$. In addition, we showed that this linear space is the complement of certain regular hyperbolic plane in the sense of Graves $[5]$ with respect to a finite projective plane.