I have recently calculated three linearly independent Killing vector fields on a G^2 manifold with a specific metric, which can be found in this paper:

https://arxiv.org/pdf/hep-th/0011256.pdf

The metric can be found on page 13. In the coordinates used there, the Killing vector fields I found were:

$$\frac{\partial}{\partial \psi}, \hspace{.5cm} \frac{\partial}{\partial \tilde{\psi}}, \hspace{.5cm} \frac{\partial}{\partial\phi} + \frac{\partial}{\partial\tilde{\phi}}$$

I was wondering if anyone could tell me what the physical significance of these might be? For example, in General Relativity, a killing vector may represent the direction of time. I know that they generate flows which are the isometries on the manifold but am wondering if there is any easy way to describe what that would entail physically if physics could work on this manifold.