Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 1 / 11E / i / Solution Created 2026-09-24 Updated 2026-09-25
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A regularly parametrized curve on an embedded surface is a geodesic when its covariant acceleration vanishes. Equivalently, in the ambient Euclidean space,
(1)
for an affine geodesic parameter. A complete geodesic is one whose maximal affine parameter interval is all of .
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