On Convex Projective Manifolds and Cusps

Daryl Cooper; Darren Long; Stephan Tillmann

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arXiv · 1109.0585

On Convex Projective Manifolds and Cusps

Daryl Cooper·Darren Long·Stephan Tillmann

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Abstract

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.

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BibTeX RIS

Daryl Cooper, Darren Long, Stephan Tillmann. 2011-09-03. On Convex Projective Manifolds and Cusps. https://arxiv.org/abs/1109.0585

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