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I Is there any 2D surface whose metric tensor is eta?

  1. Jun 9, 2016 #1
    Does there exist any 2D surface whose metric tensor is,
    ##\eta_{\mu\nu}=
    \begin{pmatrix}
    -1 & 0 \\
    0 & 1
    \end{pmatrix}##
     
  2. jcsd
  3. Jun 9, 2016 #2

    haushofer

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    Yes. Two-dimensional flat spacetime. Or the worldsheet of a string. What are you looking for in particular?
     
  4. Jun 9, 2016 #3
    I am looking for a surface in 'space'.
     
  5. Jun 9, 2016 #4

    Orodruin

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    Staff Emeritus
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    Your question is unclear. If you are asking if you can get that metric on a two-dimensional surface induced by its embedding in a higher-dimensional Euclidean space, then no. The metric tensor induced by an embedding in a Riemannian space is going to be positive definite.
     
  6. Jun 9, 2016 #5

    haushofer

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    Science Advisor

    You mean ordinary space? But you have a Lorentzian signature. Seems to me like looking for complex Majorana spinors.
     
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