  This study of properly or strictly convex real projective manifolds
introduces notions of parabolic, horosphere and cusp. Results include a
Margulis lemma and in the strictly convex case a thick-thin decomposition.
Finite volume cusps are shown to be projectively equivalent to cusps of
hyperbolic manifolds. This is proved using a characterization of ellipsoids in
projective space.
  Except in dimension 3, there are only finitely many topological types of
strictly convex manifolds with bounded volume. In dimension 4 and higher, the
diameter of a closed strictly convex manifold is at most 9 times the diameter
of the thick part. There is an algebraic characterization of strict convexity
in terms of relative hyperbolicity.
