Timeline for Understanding the Lie derivative by multivector fields
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Dec 10 at 19:20 | comment | added | Pedro Lauridsen Ribeiro | What about $2p$-vector fields with $p>1$ then? | |
| Dec 10 at 17:45 | comment | added | mlainz | This follows from $[X\wedge Y,Z] = X\wedge [Y,Z] \pm [X,Z]\wedge Y $ (see [1]) | |
| Dec 10 at 17:42 | comment | added | mlainz | This does not generalize to $p$-vector fields with $p>2$. One can compute that if $X = X_1 \wedge X_2 \wedge X_3$ then $[X,X] = 0$ always. | |
| Dec 9 at 19:07 | comment | added | Pedro Lauridsen Ribeiro | This MO question might be of interest: mathoverflow.net/q/155989/11211 - In that regard, it can be shown that a 2-vector field $X=X_1\wedge X_2$ defines an integrable 2-dimensional distribution iff its Schouten-Nijenhuis bracket with itself vanishes everywhere. This also provides a characterization of when a 2-vector field is a Poisson tensor, check e.g. P. W. Michor, Remarks on the Schouten-Nijenhuis bracket, Rend. Circ. Mat. Palermo Suppl. 16 (1987), pp. 207-215, dml.cz/dmlcz/701423 . I don't know of a similar geometric interpretation of $p$-vector fields for $p>2$. | |
| S Dec 9 at 16:53 | history | edited | R.P. | CC BY-SA 4.0 |
corrected spelling in title
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| S Dec 9 at 16:53 | history | suggested | J. W. Tanner | CC BY-SA 4.0 |
corrected spelling in title
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| Dec 9 at 16:46 | review | Suggested edits | |||
| S Dec 9 at 16:53 | |||||
| Dec 9 at 16:29 | history | asked | mlainz | CC BY-SA 4.0 |