Mathematics – Geometric Topology
Scientific paper
2011-09-03
Mathematics
Geometric Topology
51 pages, 10 figures
Scientific paper
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.
Cooper Daryl
Long Darren D.
Tillmann Stephan
No associations
LandOfFree
On Convex Projective Manifolds and Cusps does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On Convex Projective Manifolds and Cusps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Convex Projective Manifolds and Cusps will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-147730