Euclidean metric
= Euclidean metric
{c}
{title2=$\delta_{ij}dx^idx^j$}
The Euclidean metric is the constant <Riemannian metric> on $\mathbb R^n$ given in Cartesian coordinates by $g=\sum_i(dx^i)^2$. Its <Levi-Civita connection> has zero <Christoffel symbols> in those coordinates, so it is flat and its geodesics are straight lines. The <Euclidean norm> is the pointwise length determined by this metric.