I have a Riemannian metric $h$ on $\mathbb{R}$, where $h$ is as
$$ \begin{align*} h= \left(\begin{matrix} \frac{1}{\frac12+y^2} & 0 & 0\\ 0 & \frac{1}{\frac12+x^2} & 0\\ 0 & 0 & \frac{1}{k-(x^2+y^2)} \end{matrix}\right)\end{align*},$$ with constant $k$. I found the geodesics as straight lines! But what is an interpretation for a non-Euclidean Riemannian metric with straight lines as geodesics.