Deforming convex projective manifolds

Abstract

We study a properly convex real projective manifold with (possibly empty) compact, strictly convex boundary, and which consists of a compact part plus finitely many convex ends. We extend a theorem of Koszul which asserts that for a compact manifold without boundary the holonomies of properly convex structures form an open subset of the representation variety. We also give a relative version for non-compact (G,X)-manifolds of the openess of their holonomies.

Exposition improved and references added

References in corpus (1)

• Finite Volume Properly Convex Deformations of the Figure-eight Knot

Cited by in corpus (5)

• Convex projective structures on non-hyperbolic three-manifolds
• Ubiquitous quasi-Fuchsian surfaces in cusped hyperbolic 3-manifolds
• Generalized Cusps in Real Projective Manifolds: Classification
• Convex projective manifolds with a cusp of any non-diagonalizable type
• Constructing convex projective 3-manifolds with generalized cusps