All Questions

I believe that a catenoid supports a parametrization $\sigma : U \subset \mathbb{R}^2 \rightarrow \mathbb{R}^3$ that forms a conjugate system (i.e., $\sigma_{uv} \in\mathrm{span}(\sigma_u, \sigma_v)$) ...

I'm researching on discrete/semi-discrete/smooth differential geometry. Recently, I could simplify one of my geometric problems (in the smooth scenario) into the solutions of a system of linear PDEs ...

Or equivalently, why is jacobi identity equivalent to integrability of system? How do I understand it intuitively? Thanks.