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 1d awarded Commentator Jan 31 comment geodesic computation: “energy” minimization versus arc length minimization That sounds reasonable, but what does that have to do with the energy functional? It is indeed straightforward to write down the ODE satisfied by a geodesic parameterized by one of the coordinates, and indeed the ODE is not the Euler-Lagrange equation of the energy functional. That's not surprising since the energy functional is not invariant under changes of parameterization (in contrast to the length functional). Jan 30 comment geodesic computation: “energy” minimization versus arc length minimization Why would you want to restrict the parameter like that? Jan 30 comment Harmonic map into $S^n \times \mathbb{R}$ First do it using a particular choice of local coordinates on $S^n$, where you can write the metric and Christoffel symbols explicitly. Use them to derive the equation. Use stereographic projection to write the equation in terms of the map written as a map from $\Sigma$ into $\mathbb{R}^{n+2}$. Apr 15 comment Lower order perturbations of 2nd order differential operators If this is question is about whether the operator is formally self-adjoint, you should be able to do the calculation yourself. Mar 28 comment freedom in choosing a smooth function of compact support This is not appropriate for this site. Besides have you tried this when $n=1$? Feb 11 comment Flat vector bundles and constant transition functions Well, it is a consequence of the first part. Did you figure it out on your own? Again the proof is similar to an analogous description of flat Riemannian manifolds. Feb 11 comment Flat vector bundles and constant transition functions In particular, you've probably learned that a Riemannian metric is flat iff its curvature vanishes. The proof is basically the same. Feb 11 comment Flat vector bundles and constant transition functions This site is for research level questions. One like yours is for me borderline but you should at least look for references elsewhere. Or try to prove it yourself. Here's the Wikipedia article: en.m.wikipedia.org/wiki/Flat_vector_bundle Feb 6 comment definition of derivative of a vector field It's fine but if $V$ is a vector field on $M$, $dV: T_*M \rightarrow T_*(T_*M)$ and it is often not what is needed in a specific situation. Jan 3 comment Inverse of a matrix Have you tried some low-dimensional cases with explicit values for $M$ and $N$? Jun 20 comment What is name/references of inequality bounding sup-norm by $L_2$ norm (or a similar variant of this)? For a finite dimensional space, this holds for any two norms. Just compare the unit balls. Apr 27 answered Distributional/weak time derivative basic question Dec 23 awarded Supporter Oct 31 awarded Teacher Oct 31 answered Explanation about frames as distinct from a co-ordinate system