Recent content by honeytrap

Yes, in 2 dimensions the Gaussian curvature (K) can be directly derived from the Riemann curvature (R) by K=-R. Thus, there is no isometry between those two spaces. But conformal transformations are only angle preserving and do not preserve distances. So I believe that there must be a conformal...

i) Sorry, I posted the wrong metrics. Here are the correct two metrics: http://tbf.me/a/Bu4jVZii) Here are the two penrose diagrams (I believe they are correct): http://tbf.me/a/BntYLL In both diagrams the red line is a horizon (chronology/ cauchy). Could someone help me read/ compare the...

They are not asymptotically flat because of the identification of one coordinate; I call it asymptotically flat under identification. But without the identification they would be both asymptotically flat.

By 2-dimensions I mean a 2-dim manifold with Lorentz metric (-,+). As a mathematician, I am not familiar with the Penrose diagrams, so I didn't draw them. I thought there might be a necessary requirement/ premise or assumption so that we can conclude a "conformal relation". But, what kind of...

I have two 2-dimensional space-times. One of them is flat the other one has not-vanishing curvature (Riemann tensor). But they seem to have a similar global and causal structure. Of course, because of the 2-dimensional case they are local conformally flat. I am looking for a relation between...

This means then that it doesn't make sense to calculate the shape operator at all? Or is there a canonical embedding that could be picked (e.g. 3-dim Euclidean/ Minkowski space)? The computation would depend on the embedding and thus the result would not deliver any general information that...

Thanks for your answer! I am actually interested in the 2-dimensional (u,v)- "Schwarzschild" manifold (surface) defined by the metric above. From the shape operator (e.g. the eigenvalues = principal curvatures) you can derive the Gaussian curvature and the mean curvature. I computed the Ricci...

Hello: I would like to understand how to compute the shape operator (and eigenvalues etc) for a complex example like the Schwarzschild spacetime. It's easy for a submanifold in Euclidean space, but I don't know how to do it for the more advanced examples like the schwarzschild spacetime in...