  Any germ of a complex analytic space is equipped with two natural metrics:
the outer metric induced by the hermitian metric of the ambient space and the
inner metric, which is the associated riemannian metric on the germ. These two
metrics are in general nonequivalent up to bilipschitz homeomorphism. We give a
necessary and sufficient condition for a normal surface singularity to be
Lipschitz normally embedded (LNE), i.e., to have bilipschitz equivalent outer
and inner metrics. In a partner paper [15] we apply it to prove that rational
surface singularities are LNE if and only if they are minimal.
