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Domain of the exponential map

The domain of

exp_{p}

is the star-shaped open set

D_{p} = {v \in T_{p} M : γ_{v} exists on [0, 1]} .

Smooth dependence for ordinary differential equations makes

(p, v) \mapsto exp_{p} (v)

smooth on its open domain in

TM

.

Table of contents 72 1
- Exponential map of the punctured plane Domain of the exponential map 41

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