Timeline for Vector Laplace Beltrami operator of the Gauss map
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Jan 11, 2018 at 16:20 | comment | added | Robert Bryant | @BuyangLI: Since the derivation of the formula is a straightforward calculation and since you know how to prove it, you could just say 'By a straightforward calculation...". I don't know why you need to cite a reference. If a referee objects, then you can just put in the calculation, which only takes a paragraph or so. Maybe it's true that the formula for only a surface in flat $3$-space is not written explicitly in many places, but a book that gives the calculation of $\Delta N$ for general hypersurfaces in general Riemannian manifolds will contain this formula as a special case. | |
| Jan 11, 2018 at 15:47 | comment | added | Buyang LI | We have looked at many books, but still have not found this formula. | |
| Jan 11, 2018 at 15:36 | comment | added | Buyang LI | Thank you very much. Actually we can prove it, but we don't know how to cite this in our paper as we do not want to prove it in our paper... | |
| Jan 11, 2018 at 13:17 | comment | added | Robert Bryant | @BuyangLI: I don't know a specific reference in the literature, but, because the formula is so easy to derive using the structure equations, I believe that it will be found in any practically paper or book that has a need for it. If it will be useful to you, I can add the calculation as a paragraph at the end of my answer. | |
| Jan 11, 2018 at 10:52 | comment | added | Buyang LI | Dear Robert, could you please give us a citable reference for this formula ? Many thanks! | |
| Jul 29, 2014 at 7:05 | vote | accept | madison54 | ||
| Jul 28, 2014 at 15:44 | history | answered | Robert Bryant | CC BY-SA 3.0 |