Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 2 / 26I / a / Solution

For $v\in T_p\Sigma$, let ${\gamma }_v$ be the maximal geodesic with ${\gamma }_v(0)=p$, ${\dot{\gamma }}_v(0)=v$. Then ${\exp }_p(v)={\gamma }_v(1)$ on the open star-shaped set of $v$ for which time $1$ exists.

Solved by gpt-5.6-sol high.