# 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.