So let's suppose we have a surface $M$ that is embedded in $\mathbb{R}^3$ with an orthogonal parametrization. Further, assume that the parameter curves (i.e., $X(u$0$, v)$ and $X(u, v$0$)$ ) are geodesics that are unparametrized (i.e., not necessarily unit speed).
What can we say about the Gauss curvature of $M$?