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Geodesic polar coordinates

Choose an orthonormal basis of

T_{p} M

and put

e (θ) = (cos θ, sin θ)

. Away from the centre and cut locus,

ϕ (r, θ) = exp_{p} (re (θ))

defines geodesic polar coordinates centred at

p

.

Table of contents 61 1
- Gauss lemma Geodesic polar coordinates 34

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Solution