Let $I$ and $J \subset \mathbb{R}$ be two intervals of the real line. A smooth parametrized immersed surface $\sigma: I\times J \rightarrow \mathbb{R}^3$ is called a surface of Voss if its coordinate curves satisfy the following conditions:
- They form a conjugate net (i.e. $\sigma_{uv} \in \textrm{span}\{\sigma_u, \sigma_v\}$),
- They are two one-parameter families of geodesics.
I'm looking for non-trivial examples (non-developable surfaces) of this kind. I would be very much interested in a non-minimal example too.
My Attempt: I know that there are ways of making them using their relation to a pseudospherical surface but all of them involve solving systems of PDEs and I wish to know if one has a "relatively simple" example of these surfaces.