Area minimizing projective planes on the projective space of dimension 3 with the Berger metric

Area-minimizing Projective Planes in Three-manifolds

On the convex hull of projective planes

We study the finite projective planes with linear programming models. We give a complete description of the convex hull of the finite projective planes of order 2. We give some integer linear programming models whose solution are, either a finite projective (or affine) plane of order n, or a (n + 2)-arc.

Embeddings of Projective Klingenberg Planes in the Projective Space PG(5,K)

In this paper embeddings of projective Klingenberg planes in a 5-dimensional projective space are classified. It is proved that if a PK-plane is fully embedded in PG(5,K), for some skewfield K, then it is either isomorphic to the Desarguesian projective Klingenberg plane (projective Hjelmslev plane for bijective σ) PH(2,D(K, σ)) over a ring of ordinary or twisted dual numbers or it is a subgeom...

Classification of Embeddings of the Flag Geometries of Projective Planes in Finite Projective Spaces, Part 3

The flag geometry 1=(P, L, I) of a finite projective plane 6 of order s is the generalized hexagon of order (s, 1) obtained from 6 by putting P equal to the set of all flags of 6, by putting L equal to the set of all points and lines of 6, and where I is the natural incidence relation (inverse containment), i.e., 1 is the dual of the double of 6 in the sense of H. Van Maldeghem (1998, ``General...

Projective Planes of Type

During the last few years, there has been a mild surge of interest in projective planes of type I-4. This paper is intended to both provide a survey of some recent theorems, and to present some new results concerning these planes. In Section 2, we describe the algebraic setting for these planes. Special attention is given to the structure of the relevant homology groups. In Section 3, some rece...