论文标题
在带有阳性标态曲率的3个manifolds中，在Riemannian Polyhedra上具有非obtuse二面角
On Riemannian polyhedra with non-obtuse dihedral angles in 3-manifolds with positive scalar curvature
论文作者
论文摘要
我们确定r^3中所有3维简单凸的组合类型的组合类型，这些凸层可以实现为平均曲率凸（或完全测量的）riemannian polyhedra，在Riemannian 3- manifolds中具有非obtuse Dihedral Angles，具有正标量曲率。该结果可以被视为在三维双曲线多面体上的Andreev定理的类似物。此外，我们构建了许多在较高维度中的简单凸多型的示例。
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.
