Hello, I am looking for some nontrivial metric on ℝ^2 invariant under the coordinate transformations defined by the 2x2 matrix(adsbygoogle = window.adsbygoogle || []).push({});

[1 a_{12}(θ)]

[a_{21}(θ) 1],

where a_{ik}is some real function of θ. In the same way that the Minkowski metric on ℝ^2 is invariant under Lorentz transformations.

Does this metric exist? If not does it exist for some related type of transformations? And why? Are there some other nice features about this kind of transformations/matrices?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A Invariant metric

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**