Coordinates of Point of Reference of Normal Neighborhood
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Theorem
Let $\struct {M, g}$ be an $n$-dimensional Riemannian manifold.
Let $U_p$ be the normal neighborhood for $p \in M$.
Let $\struct {U_p, \tuple {x^i} }$ be any normal coordinate chart.
Then the coordinates of $p$ are $\tuple {0, \ldots, 0}$.
Proof
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Sources
- 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 5$: The Levi-Civita Connection. Normal Neighborhoods and Normal Coordinates