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arXiv · 2201.06059

On Riemannian polyhedra with non-obtuse dihedral angles in 3-manifolds with positive scalar curvature

Li Yu
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Abstract

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.

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Li Yu. 2022-01-16. On Riemannian polyhedra with non-obtuse dihedral angles in 3-manifolds with positive scalar curvature. https://doi.org/10.1007/s00229-023-01501-7

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