2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/209852For every diffeomorphism $φ:M\to N$ between 3--dimensional Riemannian manifolds $M$ and $N$ there are in general locally two 2--dimensional distributions $D_{\pm}$ such that $φ$ is conformal on both of them. We state necessary and sufficient conditions for a distribution to be one of $D_{\pm}$. These are algebraic conditions expressed in terms of the self-adjoint and positive definite operator $(φ_{\ast})^*φ_{\ast}$. We investigate integrability condition of $D_+$ and $D_-$. We also show that it is possible to choose coordinate systems in which leafwise conformal diffeomorphism is holomorphic on leaves.12 pagesDifferential Geometry53A30, 53C12, 53B20text