Frobenius conjugation and Jacobi functions for minimal immersions in $\mathbb{S}^3$ and CMC $1$ immersions in $\mathbb{R}^3$

We give a first-order Frobenius description of conjugate minimal immersions in the round three-sphere and use it to define the conjugate of an arbitrary Jacobi function. The construction is intrinsic at the linearized level and does not require the Jacobi function to be integrable through a normal d