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

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1. Jun 9, 2016

### arpon

Does there exist any 2D surface whose metric tensor is,
$\eta_{\mu\nu}= \begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}$

2. Jun 9, 2016

### haushofer

Yes. Two-dimensional flat spacetime. Or the worldsheet of a string. What are you looking for in particular?

3. Jun 9, 2016

### arpon

I am looking for a surface in 'space'.

4. Jun 9, 2016

### Orodruin

Staff Emeritus
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.

5. Jun 9, 2016

### haushofer

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