bio | website | |
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location | ||
age | ||
visits | member for | 2 years, 3 months |
seen | Jan 22 at 1:20 | |
stats | profile views | 81 |
Sep 7 |
awarded | Curious |
Sep 6 |
asked | Casimirs of Poisson brackets obtained via Poisson reduction |
Apr 17 |
accepted | Zero currents localized along a submanifold |
Apr 17 |
comment |
Zero currents localized along a submanifold
The hitch in this definition of $\mathcal{L}_Xs$ is that $s(\phi^X_t(m))$ and $s(m)$ live in different fibers of $E$, and so can't be subtracted. However, when $E$ is a bundle of tensors (and $\mathcal{L}_X$ is the vanilla Lie derivative), I now understand that your ansatz for $u$ is indeed the most general $u$ localized along $S$. Thank you again! |
Apr 17 |
comment |
Zero currents localized along a submanifold
Thanks very much! I have a couple of questions about your response. (i) I'm not sure how those Lie derivatives act on sections of the general vector bundle $E$; if $E$ is not a bundle of tensors, should these be covariant derivatives relative to some connection on E? (ii) If we don't introduce a metric on $M$, do you think the global characterization can be expressed in terms of sections of the abstract normal bundle $(\iota_S^*TM)/TS$? |
Apr 16 |
asked | Zero currents localized along a submanifold |
Jan 17 |
revised |
Is the time derivative of the WKB phase globally defined?
fixed minor error; forgot a factor of 2pi |
Jan 17 |
asked | Is the time derivative of the WKB phase globally defined? |
Nov 5 |
comment |
non-zero, divergence-free vector fields on 2-torus
Thanks very much for your answer. It's pretty slow going for me as I now look through the literature in order to find a more detailed description of why this is true. Could you possibly point me to a reference, maybe a textbook? |
Nov 5 |
awarded | Scholar |
Nov 5 |
awarded | Supporter |
Nov 4 |
asked | non-zero, divergence-free vector fields on 2-torus |
Oct 26 |
comment |
Curl operators parameterized by the set of Riemannien metrics on a 3-manifold
@Paul Reynolds : Sorry for not being clear. I'm not requiring the volume form to be the one determined by the metric. |
Oct 25 |
revised |
non-vanishing magnetic helicty density
another example |
Oct 25 |
revised |
Curl operators parameterized by the set of Riemannien metrics on a 3-manifold
hopefully clarified question |
Oct 25 |
asked | Curl operators parameterized by the set of Riemannien metrics on a 3-manifold |
Oct 19 |
revised |
non-vanishing magnetic helicty density
slight generalization of question |
Oct 19 |
revised |
non-vanishing magnetic helicty density
corrected an error |
Oct 19 |
revised |
non-vanishing magnetic helicty density
minor correction |
Oct 16 |
comment |
Variational problems whose lagrangian density depends on derivatives higher than 1.
Higher order derivatives can be treated in an intrinsic manner using jet bundles. gmcnetwork.org/files/thesis/cmcampos.pdf Page 78 of this thesis describes a nice approach to variational calculus using this sort of machinery. |