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Mathematics > Differential Geometry

arXiv:2201.06059 (math)
[Submitted on 16 Jan 2022 (v1), last revised 14 Jun 2022 (this version, v3)]

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

Authors: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.
Comments: 20 pages, 11 figures. Minor revisions are made
Subjects: Differential Geometry (math.DG); Geometric Topology (math.GT)
MSC classes: 51M20, 51F15, 52B10, 53C23, 57M50, 57S12
Cite as: arXiv:2201.06059 [math.DG]
  (or arXiv:2201.06059v3 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.2201.06059
Journal reference: Manuscripta Mathematica 174(1-2): 269-286, 2024
Related DOI: https://doi.org/10.1007/s00229-023-01501-7

Submission history

From: Li Yu [view email]
[v1] Sun, 16 Jan 2022 14:46:20 UTC (240 KB)
[v2] Sat, 9 Apr 2022 13:00:31 UTC (873 KB)
[v3] Tue, 14 Jun 2022 02:02:52 UTC (879 KB)
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