Recent content by Fgard

I am going through Almheriri's article about " Models of AdS##_2## and I am stuck on a derivation. I think they make some kind of assumption which I don't understand. What I am trying to do, is to compute the equation of motion by varying the action with respect to the metric. Unfortunately I...

Okej, so I have to choose a definition for the differential map and show that map dose not depend on a certain choice of chart. Thanks.

I am taking my first graduate math course and I am not really familiar with the thought process. My professor told us to think about how to prove that the differential map (pushforward) is well-defined. The map $$f:M\rightarrow N$$ is a smooth map, where ##M, N## are two smooth manifolds. If...

Thanks for your help andrewkirk, it cleared up my confusion with the Lie bracket. I see now that i forgot to mention in my initial post that: $$X,Y\in V_K(M)$$ and $$Z\in V(M)$$ With K as the characteristic distribution of ##\sigma## and X,Y are tangent to this distribution.

I am trying to prove the following: $$3d\sigma (X,Y,Z)=-\sigma ([X,Y],Z)$$ where ##X,Y,Z\in\mathscr{X}(M)## with M as a smooth manifold. I can start by stating what I know so it is easier to see what I do wrong for you guys. I know that a general 2-form has the form...

Okej. Thank you very much for all the help.

So that [tex]$\Psi$[\tex] maps between different subsets comes from a definition?

I am studying differential geometry and I stumbled on something that I don't understand. When we have a m- dim differential manifold, with U_i and U_j open subsets of M with their corresponding coordinate function phi. As can be seen in the figure. If I understand it correctly phi_j of a...

Thanks for the tip. I will check out the book.

I am taking my bachelor in geometric quantization but I have no real experience in differential geometry ( a part of my project is to learn that). So I find myself in need of some good books that cover that the basics and a bit more in depth about symplectic manifolds. If you have any...

I think I solved it. Thanks for all the help!

That is what I have trying to do, quite unsuccessfully so far. But I know now at least that this is the way to do it, so thank you.

No one that can help me?

The upper limit of the summation is suppose to be l. I have singularity there, so the constant B has to be zero. Thanks.

Homework Statement Solve the Laplace equation inside a sphere, with the boundary condition: \begin{equation} u(3,\theta,\phi) = \sin(\theta) \cos(\theta)^2 \sin(\phi) \end{equation} Homework Equations \begin{equation} \sum^{\infty}_{l=0} \sum^{m}_{m=0} (A_lr^l + B_lr^{-l -1})P_l^m(\cos...