Convex projective structures on Gromov–Thurston manifolds
نویسندگان
چکیده
Gromov and Thurston in [10] constructed, for each n 4, examples of compact n– manifolds which admit metrics of negative curvature, with arbitrarily small pinching constants, but do not admit metrics of constant curvature. We review these examples in Section 3. The main goal of this paper is to put convex projective structures on Gromov– Thurston examples. Suppose that RP is an open subset and PGL.nC1;R/ is a subgroup acting properly discontinuously on . The quotient orbifold QD= has the natural projective structure c . The structure c is said to be (strictly) convex iff is a (strictly) convex proper subset of RP . In this case we refer to Q as (strictly) convex projective orbifold.
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