 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-2/26i/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

For

v \in T_{p} Σ

, let

γ_{v}

be the maximal geodesic with

γ_{v} (0) = p

\overset{γ}{˙}_{v} (0) = v

. Then

exp_{p} (v) = γ_{v} (1)

on the open star-shaped set of

v

for which time

1

exists.

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