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The failure is actually more profound than you might guess at first glance: There are conformal metrics on the Poincare disk that cannot (even locally) be isometrically induced by embedding in $\ma …

While it's good to have a source, such as Datta's paper that points out the error, I find that his explanation of why the key equation is wrong is not as clear as it could be. In fact, with a little …

in addition to these excellent examples of non-local curvature quantities and their extensions to the non-smooth setting (which I am not sure the OP was anticipating), I might add the 'original' non-l …

My guess is that Weinstein was thinking of this fact, but didn't get it out correctly: For every $n\not=15$, there is a compact Lie group $H_n\subseteq\mathrm{SO}(n{+}1)$ that acts transitively on the …

This is about your specific question. For any vector space $V$ of dimension $n$, one has canonical decompositions $$ S^2(S^2V^*) \simeq S^4(V^*)\oplus K(V^*) $$ and $$ S^2(\Lambda^2V^*) \simeq \Lamb …

There is an elementary proof in our 2003 book Exterior Differential Systems and Euler-Lagrange Partial Differential Equations (Bryant, et al, University of Chicago Press). It does not use any represen …

Answers to the OP's question depend on where the OP is willing to start. To prove that an abstractly defined group is (i.e., has the structure of) a Lie group, one will have to use something nontrivi …

If all you really want to know are the irreducible representations of ${\frak{so}}(7)$ and ${\frak{so}}(8)$ up to dimension $30$, I can save you the trouble of looking up these tables: For ${\frak{so …

Your two final questions are not the same, in spite of the "That is,..." that starts the second one, but, in the interpretations that make the most sense to me, the answer to the first is 'no' and the …

There's a different kind of answer to this that you might be interested in: Suppose that, when you fire off a probe along a unit speed geodesic starting at $p\in M$, you record the direction $\theta$ …

The question you are asking is a very basic one in the theory of what Élie Cartan called "the method of the moving frame" (in the original French, "la méthode du repère mobile"), so you should be look …

Looking around on the internet, I found an English translation of Lie's 1891 paper Die Grundlagen für die Theorie der unendlichen kontinuierlichen Transformationsgruppen. I. (I.e., The foundations of …

In this particular case, the invariant theory is pretty simple, so there is an explicit description. Recall that, in general, for a homogeneous space $M=G/H$, a $G$-invariant, $m$-th order linear d …

Probably, you can find a discussion of this in Thurston's notes on hyperbolic 3-manifolds, or maybe some of the expositions by his students. However, what you are asking for is actually pretty simple: …

Using the reference https://arxiv.org/pdf/0903.2087.pdf, which agrees with https://arxiv.org/pdf/hep-th/0001078v1.pdf, which agrees with the reference U. Müller, C. Schubert and Anton M. E. van de Ven …