Timeline for Mean curvature under conformal transformation
Current License: CC BY-SA 4.0
3 events
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| Oct 13, 2022 at 17:59 | comment | added | Willie Wong | For that particular answer: read the commends and discussion between the OP and Robert Bryant. The problem is that it is very easy to make a mistake (between covariance and contravariance) in these types of calculations, and sometimes it is easier to re-base using a new frame then trying to remember exactly where the $e^{2f}$ go in every single step. | |
| Oct 13, 2022 at 16:03 | comment | added | Leo Moos | I think the point is that with an orthonormal frame the mean curvature is just $H = \sum_i h_{ii}$ (or $H = \frac{1}{n} \sum_i h_{ii}$, depending on the convention). In a general frame $H = \operatorname{tr}_g A = g^{ij}h_{ij}$, with summation over repeated indices. (Again, depending on your convention, you'd have to normalize by $n$ here too.) | |
| Oct 13, 2022 at 15:47 | history | asked | Tree23 | CC BY-SA 4.0 |