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Nov
13
comment How to prove this formula for Lie Derivative for differential forms
@FlybyNight I believe $\phi_t$ in my notation is the $f$ in your notation. And $\phi_t^* w$, viewed as a whole thing, is exactly the $w^*$ in your notation. $\phi_t^*$ is the mapping that takes $ w$ to $w^*$. But never mind, I know how to prove this thing now. It's only a simple computation once you know what all those mappings really are. Thanks anyway.
Nov
13
revised How to prove this formula for Lie Derivative for differential forms
edited body
Nov
13
comment How to prove this formula for Lie Derivative for differential forms
@FlybyNight huh? $w$ here is a differential form.
Nov
12
asked How to prove this formula for Lie Derivative for differential forms
Sep
26
accepted How do I see that the tangent bundle of torus is trivial
Sep
26
comment How do I see that the tangent bundle of torus is trivial
Thanks, @Neal, for providing so many ways of seeing it
Sep
26
comment How do I see that the tangent bundle of torus is trivial
@RyanBudney Thanks! I guess that's one way of doing it.
Sep
26
comment How do I see that the tangent bundle of torus is trivial
what do you mean by taking one vector field in the direction of each "factor"?
Sep
26
asked How do I see that the tangent bundle of torus is trivial
Sep
10
accepted How to show the height function of a torus has 4 critical points
Sep
10
comment How to show the height function of a torus has 4 critical points
Thank you. I wasn't aware of this form before.
Sep
10
comment How to show the height function of a torus has 4 critical points
Thanks, @t.b.! I will take a look.
Sep
10
asked How to show the height function of a torus has 4 critical points
Aug
1
accepted generalized Rayleigh Quotient
Aug
1
comment generalized Rayleigh Quotient
Thank you! I didn't check it in detail, but looks right to me. And about that change of scalar product, that's similar to the answer Will Jagy gave. but since you are the only one answering the problem in a direct way, i will pick your answer as the best one. Thank you!
Aug
1
comment generalized Rayleigh Quotient
why is that for any $y\in A$, $y$ can be written as $y=h-(h,f)f$, while your $h$ here in any vector in $X$?
Jul
27
accepted Proof of Gauss's Lemma (Riemannian Geometry version)
Jul
27
comment Proof of Gauss's Lemma (Riemannian Geometry version)
Now that you confirmed what I wrote was right, there's definitely some mistake in Wiki. Thanks a lot. For beginners like me, some times it's hard to tell right from wrong.
Jul
27
comment Proof of Gauss's Lemma (Riemannian Geometry version)
I think the result should be the parallel transport of $v$ along the geodesic at the point $\exp_p(v)$. This makes sense, and it yields what I need. Because Parallel transportation preserves the inner product if the connection is compatible with the metric.
Jul
27
comment Proof of Gauss's Lemma (Riemannian Geometry version)
@ZhenLin Thank you for the clarification!