Timeline for Hilbert's Theorem relevance to positive curvature
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Oct 9, 2014 at 9:09 | comment | added | Vladimir S Matveev | May be missunderstanding is due to different definitions? Because for me a sufrace isometric to the round sphere is necessary complete since completeness is for me a metric property and the round sphere is complete in the metric sense which implies that anything isometric to the round sphere is also complete which contradicts what you wrote in your comment. What is your definition of completeness? | |
| Oct 8, 2014 at 15:42 | comment | added | Narasimham | Either for K=1 or K=-1 in $ k_1 k_2 = K = constant $ $ k_1 $ goes to infinity when $ k_2 $ goes to zero producing cuspidal boundaries which demarcate periodic segments of an otherwise regular surface. Apart from above example Sievert surface also has a cuspidal edge...they are not complete regular even though isometric to round ball. | |
| Oct 8, 2014 at 13:05 | history | answered | Vladimir S Matveev | CC BY-SA 3.0 |