98 reputation
5
bio website
location
age
visits member for 2 years, 5 months
seen yesterday

Feb
26
comment Obstruction to the existence of global isometries on a constant-curvature Riemannian manifold
@ThiKu your point is well-taken. However I wonder if there is a terminology issue here. There are apparently two kinds of "Killing vectors", those with complete flows and those without. The ones with complete flows are special because they are elements of the Lie algebra of the isometry group. Are both types of vectors commonly referred to as "Killing vectors"?
Feb
26
comment Obstruction to the existence of global isometries on a constant-curvature Riemannian manifold
Thank you. This answer together with the comments above have greatly cleared up a lot of my confusion. But how can we tell which, if any, of the pulled-back killing vectors are genuine Killing vectors on $M^m$? For instance, suppose $m=2$, $k=1$, and $dev(M^m)$ is the domain of the stereographic projection $S^2\rightarrow\mathbb{R}^2$. The killing vector that fixes the north pole will pull back to a genuine killing vector, but the others would not.
Feb
26
asked Obstruction to the existence of global isometries on a constant-curvature Riemannian manifold
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