关于正数量曲率3-流形中具有非钝二面角的黎曼多面体
On Riemannian polyhedra with non-obtuse dihedral angles in 3-manifolds with positive scalar curvature
AI总结：
本文确定了R^3中三维简单凸多面体的组合类型，其能在正数量曲率黎曼3-流形中实现为具非钝二面角的黎曼多面体，并视为Andreev定理的类比，同时构造了高维例子。
摘要：
我们确定了R^3中所有三维简单凸多面体的组合类型，这些多面体可在具有正数量曲率的黎曼3-流形中实现为具有非钝二面角的平均曲率凸（或完全测地）黎曼多面体。该结果可视为Andreev定理关于具有非钝二面角的三维双曲多面体的类比。此外，我们在更高维中构造了许多此类简单凸多面体的例子。
英文摘要：
We determine the combinatorial types of all the 3-dimensional simple convex polytopes in R^3 that can be realized as mean curvature convex (or totally geodesic) Riemannian polyhedra with non-obtuse dihedral angles in Riemannian 3-manifolds with positive scalar curvature. This result can be considered as an analogue of Andreev's theorem on 3-dimensional hyperbolic polyhedra with non-obtuse dihedral angles. In addition, we construct many examples of such kind of simple convex polytopes in higher dimensions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
