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| bio | website | anglesmatter.wordpress.com |
|---|---|---|
| location | Auckland, New Zealand | |
| age | 45 | |
| visits | member for | 2 years, 8 months |
| seen | 7 hours ago | |
| stats | profile views | 418 |
Doing conformal geometry
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May 16 |
answered | What is a conormal vector to a domain intuitively? |
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May 13 |
comment |
(Basic) question regarding Einstein-Hilbert-functional / total scalar curvature By the way, please look at this my answer too. |
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May 12 |
comment |
(Basic) question regarding Einstein-Hilbert-functional / total scalar curvature I guess that @smiley06 speaks about L^2:={symmetric tensors on a fixed manifold with the L^2 inner product} that is easily shown to be a Hilbert space. I am not too sure if it makes sense to deal with the manifold of all Riemannian metrics but you may ask a question on that on mathoverflow.net where P.Michor is frequently seen :-) |
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May 12 |
revised |
Orientation preserving diffeomorphism. added 144 characters in body |
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May 12 |
revised |
Orientation preserving diffeomorphism. added 1828 characters in body |
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May 11 |
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(Basic) question regarding Einstein-Hilbert-functional / total scalar curvature Welcome to MathSE and thank you for you question. I admit that it is not easy to find that a very similar question has been already asked and answered here. Please look at this one. |
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May 10 |
answered | Orientation preserving diffeomorphism. |
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May 7 |
comment |
Figure $\infty$ is immersion of circle Lemniscate of Bernulli |
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Apr 30 |
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Second derivative of a metric in terms of the Riemann curvature tensor. If it helped, and you realized what was the problem, please consider adding your own answer :-) |
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Apr 30 |
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Second derivative of a metric in terms of the Riemann curvature tensor. Sorry, no time to write an answer at the moment, but you can look at this paper for a hint on p.3, or read the whole very detailed story here. |
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Apr 27 |
revised |
Justification for this manipulation in a proof of the first variation of energy formula added 1584 characters in body |
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Apr 27 |
answered | Meaning of modulo diffeomorphism |
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Apr 25 |
answered | Calculating Principal curves |
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Apr 25 |
revised |
Two results on the mean curvature of hypersurfaces added 1 characters in body |
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Apr 25 |
answered | Two results on the mean curvature of hypersurfaces |
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Apr 25 |
comment |
Zeros of the second fundamental form Thank you for sharing your thoughts. I shall definitely find some time to think about this carefully, but currently I am close to my deadline and have to work hard on my project. Feel free to edit this, add your own answers, etc. It looks like a research level question, so it may be more relevant to crosspost it to mathoverflow.net (please give the link to this question). You may get more active response there. |
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Apr 23 |
revised |
naked singularity and null coordinates Replaced the link to make the post compliant with the copyright rules. |
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Apr 22 |
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Justification for this manipulation in a proof of the first variation of energy formula In fact, I believe now that you've spotted a sloppy step in the presented calculation. It is better to use directly $\frac{d}{d s} \langle X, Y \rangle = \langle \nabla_V X, Y \rangle + \langle X, \nabla_V Y \rangle $, as in Lemma 5.2 of J.M.Lee's "Riemannian Manifolds", p.67. Effectively, you don't need the step (2) at all. |
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Apr 22 |
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Justification for this manipulation in a proof of the first variation of energy formula @Zev Sorry, you are right: $h$ is defined on the rectangle. |
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Apr 21 |
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Justification for this manipulation in a proof of the first variation of energy formula Think your $h$ defined on $M$, so that $f^* h = h \circ f$ is defined for any smooth $f$. And don't forget the Chain Rule. |
