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What is a pseudo-Euclidian cone?

  1. Mar 20, 2012 #1
    Dear Sir/Madam,
    i am doing GR just for fun and have not any degree in neither physics or mathematics. My question is simple:
    i've just started to cutting and folding the pseudo Euclidian-plane (axes x, i*z). I've found that the pseudo-Euclidian analogue of the Euclidian 2-sphere is a one-sheet hyperboloid (embedded in 3-space, axes x, y, i*z). Is the hyperbolic paraboloid (a saddle surface embedded in 3-space, axes x, y, i*z), the diffeomorphic equivalent of flat pseudo Euclidian-plane, that is to say, what a cone is to the real Euclidian plane?
    i asked this question in special & general relativity forum and got no reply! How hard is it to answer a simple question as that?
    Again, i rephrase it. In the Euclidian plane i cut an angle, apex the origin, fold the remainder of the plane around and get a cone. How do i do this in the Minkowskian plane, without any stretching of the plane? I am aware of length distortions of lines due to the - (minus) in the metric and that's not the type of stretching i'm talking about. Do not give me isometric versions of the plane, i do not care about it! i just want a surface in the Minkowski 3-plane (space).
    To get a cone, i perform just one cut in the Euclidian plane. In the Minkowskian plane, must i do 4 ?? What are they?
    If no-one bothers to answer my question again, please delete me from this forum...
  2. jcsd
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