The metric induced by the p-norm:
$d((x_1,\dotsc,x_n),(y_1,\dotsc,y_n)) = \left(\sum_{i=1}^n |x_i-y_i|^p\right)^{1/p}$
is often called the Minkowski distance.
There is also Minkowski space, which as I understand is a bit like Euclidean 4-space. And there is the Minkowski metric tensor defined for it.
Is there a relationship between Minkowski distance and the Minkowski metric tensor? If not, why is the metric induced by the p-norm called Minkowski distance? Does anybody have a reference for this name?