The Real Projective Plane

J.C. Álvarez Paiva

In this chapter we study the geometry of $n$-dimensional projective space with special emphasis on the projective plane. We change somewhat our point of view and study the projective plane not only as a homogeneous space under an action of $PGL(3,{\Bbb R})$, but also as a space with a family of distinguished subspaces (the projective lines) that satisfy a number of incidence relations.

Notes

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• Next to the exercises there is a two-digit number in parentheses which describes its degree of difficulty. The simplest exercises are identified by a (00), while the hardest -- those that could take you a week of intensive brain work -- are identified by a (50).