Timeline for Compactification of a Cartan-Hadamard manifold
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Mar 26 at 21:12 | comment | added | ZZZ | @IgorBelegradek Thanks a lot for the references! | |
| Mar 26 at 20:01 | comment | added | Igor Belegradek | A standard text for a graduate student would be "Metric Spaces of Non-Positive Curvature" by Bridson and Haefliger, which doesn't limit the discussion to Riemannian manifolds, but in fact the manifold case isn't easier. The books that focus on manifolds are "Manifolds of Nonpositive Curvature" by Ballmann, Gromov and Schroeder and Eberlein's "Geometry of Nonpositively Curved Manifolds". | |
| Mar 26 at 19:49 | comment | added | ZZZ | @IgorBelegradek Thanks for the answer! Do you have a reference about this for non-experts? | |
| Mar 26 at 16:25 | history | edited | gmvh |
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| Mar 26 at 15:34 | comment | added | Igor Belegradek | There are two issues here: existence of a geodesic joining any two points at infinity and its uniqueness. Neither one is true for general Cartan-Hadamard manifolds. Those for which any two points at infinity are joined by a geodesic are called visibility manifolds. If the manifold contains a flat strip bounded by two bi-infinite geodesics, uniqueness fails. | |
| Mar 26 at 15:27 | comment | added | Moishe Kohan | Did you think about the Euclidean plane? Do you know the flat strip theorem? | |
| Mar 26 at 15:18 | comment | added | ZZZ | Hyperbolic space is true. Also, it should be true for manifolds with $\sec \leq -1$ | |
| Mar 26 at 15:11 | comment | added | Moishe Kohan | What examples did you check? | |
| S Mar 26 at 14:49 | review | First questions | |||
| Mar 26 at 14:50 | |||||
| S Mar 26 at 14:49 | history | asked | ZZZ | CC BY-SA 4.0 |