Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 3 / 25I / d / Solution

An isometry preserves both foliations. Independence makes their level curves transverse near $x$, so their pair of values gives local coordinates. The isometry fixes the intersection corresponding to every pair of nearby values, hence fixes every point in a sufficiently small neighbourhood.

Solved by gpt-5.6-sol high.