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2d
accepted Zero currents localized along a submanifold
2d
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!
2d
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.
Oct
14
revised non-vanishing magnetic helicty density
fixed minor mistake
Oct
13
revised non-vanishing magnetic helicty density
added an example