In this paper we show that bending a finite volume hyperbolic $d$-manifold $M$ along a totally geodesic hypersurface $\Sigma$ results in a properly convex projective structure on $M$ with finite volume. We also discuss various geometric properties of bent manifolds and algebraic properties of their fundamental groups. We then use this result to show in each dimension $d\geqslant 3$ there are examples finite volume, but non-compact, properly convex $d$-manifolds. Furthermore, we show that the examples can be chosen to be either strictly convex or non-strictly convex.

中文翻译：

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双曲流形的适当凸弯

在本文中，我们显示了沿全测地超曲面$ \ Sigma $弯曲有限体积的双曲$ d $-歧管$ M $会在有限体积的$ M $上产生适当凸的投影结构。我们还将讨论弯曲流形的各种几何性质及其基本群的代数性质。然后，我们使用此结果显示每个维度$ d \ geqslant 3 $中存在有限体积的示例，但非紧致的，适当凸的$ d $流形。此外，我们表明可以将示例选择为严格凸或非严格凸。