Unsymmetrical metric

1. May 9, 2010

paweld

Could anyone give me an example of two-dimensional metric which
doesn't have any Killing vector. It's not so easy to prove that
particular metric is indeed unsymmetrical - it may be only written
in unfortunately chosen coordinates :).

Any ideas how to attack this apparently simple problem.

2. May 9, 2010

atyy

http://arxiv.org/abs/0910.0350

Section 4 has a spacetime with no Killing vectors, but it's not 2D. Maybe the reference where they show this will help?

3. May 9, 2010

Nabeshin

Indeed hard to prove... Why not just try something absurd?
$$ds^2=e^{2x^2y}\left(dx^2+dy^2\right)+cosh^2\left(x^5\right) dx dy$$

4. May 9, 2010

paweld

Maybe this - matric induced form three dimensional flat euclidan space
on two dimensional ellipsoid with three unequal sides shouldn't posses any Killing
vectors. Am I right?
(none of killing vectors of eucliden space preserves this ellipsoid)

5. May 9, 2010

Frame Dragger

Damn, I'm stumped here, but interested.