AI 中文总结
研究闭的、不可分解的、恰当凸实射影4-流形，证明其几何分解时每块是实双曲的，推广了定理到四维，还构建特定4-流形，并刻画了支持恰当凸实射影结构的紧致局部对称空间。
AI 中文摘要
我们证明，如果一个闭的、不可分解的、恰当凸实射影4-流形是几何的或在瑟斯顿意义下允许几何分解，那么每一块都是实双曲的。这将贝努瓦的一个定理推广到了四维。此外，我们构建了具有任意正偶数欧拉特征的上述类型的可定向（非双曲）4-流形。在此过程中，我们刻画了几乎支持恰当凸实射影结构的紧致局部对称空间。
英文摘要
We prove that if a closed, indecomposable, properly convex real projective $4$-manifold is geometric or admits a geometric decomposition in the sense of Thurston, then every piece is real hyperbolic. This extends a theorem of Benoist to dimension four. Moreover, we build orientable (non-hyperbolic) $4$-manifolds of the above type, with arbitrary positive, even, Euler characteristic. Finally, we characterise the compact locally symmetric spaces that virtually support properly convex real projective structures in terms of their geometry.
Comments42 pages, 2 figures, typos corrected, improved introduction
