Timeline for Is the volume form on an oriented Riemannian manifold parallel?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| S Jun 28, 2017 at 8:12 | history | suggested | Danu | CC BY-SA 3.0 |
corrected spelling of Leibniz
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| Jun 28, 2017 at 7:49 | review | Suggested edits | |||
| S Jun 28, 2017 at 8:12 | |||||
| Dec 31, 2009 at 19:09 | comment | added | Matt Noonan | @Mariano: You're right, of course. I've edited the answer to reflect the correct (lack of) signs. | |
| Dec 31, 2009 at 19:05 | history | edited | Matt Noonan | CC BY-SA 2.5 |
fixed signs
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| Dec 27, 2009 at 0:00 | comment | added | Mariano Suárez-Álvarez | Are the signs in your formula for (1) correct? I think they only appear if one insists in applying $\nabla$ only in the first factor. | |
| Dec 26, 2009 at 23:37 | comment | added | Matt Noonan | Good point! I guess I should have said "volume density"... | |
| Dec 26, 2009 at 23:00 | comment | added | José Figueroa-O'Farrill | The volume form is not an $O(n)$ invariant, though. It's an $SO(n)$ invariant. However they have the same Lie algebra and this is all that the coavariant derivative is probing. In other words, just parallel transport along a null-homotopic loop and you're set. | |
| Dec 26, 2009 at 21:47 | history | edited | Matt Noonan | CC BY-SA 2.5 |
vector --> covector
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| Dec 26, 2009 at 21:41 | history | answered | Matt Noonan | CC BY-SA 2.5 |