Convex projective structures on non-hyperbolic three-manifolds

Abstract

Y. Benoist proved that if a closed three-manifold M admits an indecomposable convex real projective structure, then M is topologically the union along tori and Klein bottles of finitely many sub-manifolds each of which admits a complete finite volume hyperbolic structure on its interior. We describe some initial results in the direction of a potential converse to Benoist's theorem. We show that a cusped hyperbolic three-manifold may, under certain assumptions, be deformed to convex projective structures with totally geodesic torus boundary. Such structures may be convexly glued together whenever the geometry at the boundary matches up. In particular, we prove that many doubles of cusped hyperbolic three-manifolds admit convex projective structures.

48 pages, 8 figures, 2 tables

References in corpus (2)

• A census of tetrahedral hyperbolic manifolds
• Deforming convex projective manifolds

Cited by in corpus (10)

• Generalized Cusps in Real Projective Manifolds: Classification
• A flat torus theorem for convex co-compact actions of projective linear groups
• Convex co-compact actions of relatively hyperbolic groups
• Codimension-$1$ Simplices in Divisible Convex Domains
• Convex projective manifolds with a cusp of any non-diagonalizable type
• Divisible convex sets with properly embedded cones
• Constructing convex projective 3-manifolds with generalized cusps
• Rigidity of convex divisible domains in flag manifolds
• Manifolds without real projective or flat conformal structures
• Rank One Hilbert Geometries