Normal coordinates at a point 
of a Riemannian manifold
are local coordinates obtained by mapping a
neighborhood of the origin in the tangent space 
into the manifold
using the exponential map. After choosing an orthonormal basis of 
, a vector with components 
is assigned to the point
 |
At 
,
the metric tensor has Euclidean components and its
first derivatives vanish. Equivalently, the Christoffel
symbols vanish at 
. Geodesics through 
are represented by straight lines through the coordinate origin.
