Timeline for Does for every vector field there always exist a volume form for which the vector field is a homothety?
Current License: CC BY-SA 3.0
4 events
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| Jan 14, 2014 at 19:23 | comment | added | Vladimir S Matveev | I am giving up for a while: I can not prove that any projective vector field is locally linearizable near points where the projective curvature does not vanish. All examples indicate that this is the case though: at the present point I can show this statement for projective structures coming from any riemannian metric, and also for the projective structure with submaximal dimension of the space of projective vector fields (the projective structure was found by Egorov and the description of their projective vector fields can be found in the recent paper of Boris Kruglikov and Dennis The. | |
| Jan 8, 2014 at 22:47 | comment | added | Vladimir S Matveev | Robert, I do not know whether answer on your question is true. I thought that I found an example when it is wrong (which of course will imply nonlinearisability of projective vector fields) but found a possible flaw there. I will continue to think about it tomorow | |
| Jan 7, 2014 at 21:52 | history | edited | Robert Bryant | CC BY-SA 3.0 |
improved the exposition
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| Jan 5, 2014 at 13:11 | history | answered | Robert Bryant | CC BY-SA 3.0 |