Tori whose covering spaces have convex distance functions (Q1099825)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Tori whose covering spaces have convex distance functions |
scientific article; zbMATH DE number 4042782
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Tori whose covering spaces have convex distance functions |
scientific article; zbMATH DE number 4042782 |
Statements
Tori whose covering spaces have convex distance functions (English)
0 references
1986
0 references
The well known theorem of Hopf, that a 2-dimensional Riemannian torus without conjugate points is flat, does not have a direct analogue for G- spaces, as Busemann has shown. A related hypothesis is given here which does allow an analogue. Namely, if a G-space is homeomorphic to a 2- dimensional torus and its universal covering space M has a point from which the distance function is convex, then M is Minkowskian.
0 references
convexity
0 references
theorem of Hopf
0 references
conjugate points
0 references
G-spaces
0 references
torus
0 references
