Timeline for "Famous" 2d Riemannian manifolds with non-constant curvature
Current License: CC BY-SA 3.0
4 events
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| May 4, 2011 at 19:48 | comment | added | Vladimir S Matveev | Dear Giovanni, I did not understand what statement should I confirm by a reference. I claimed that for an explicitly given metric one can algorithmically understand the dimension space of Killing tensors of a given degree. This is a folklore but I do not know a good reference. Now, once we have the dimensions of the spaces of Killing tensors of degree less or equal to $k$, we know whether there exists a Killing tensor of degree k by counting the dimensions. Does it help. | |
| May 3, 2011 at 18:53 | comment | added | Giovanni Rastelli | Dear Vladimir, it seems that this algorithm connects the dimension of the space of Killing tensors of any degree with their reducibility or not, at least locally. That procedure seems very much intriguing. Could you give precise references? | |
| May 3, 2011 at 10:21 | comment | added | Vladimir S Matveev | Dear Giovanni, The Killing equations is a an overdetermined linear system of PDE of finite type and in theory there exists an algorithm that decides whether a given metric admits a Killing tensor of a given degree and determine the dimension of the space of Killing tensors. Then, this algorithm also answers whether a metric admits a non-reducible Killing tensors of some degree. To be precise, the algorithm is local and gives the answer in a neighborhood of almost every point. The algorithm is computationally very hard even in simple situations. | |
| Apr 29, 2011 at 18:42 | history | answered | Giovanni Rastelli | CC BY-SA 3.0 |