  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. A complex
analytic germ is said Lipschitz normally embedded (LNE) if its outer and inner
metrics are bilipschitz equivalent. LNE seems to be fairly rare among surface
singularities; the only known LNE surface germs outside the trivial case
(straight cones) are the minimal singularities. In this paper, we show that a
superisolated hypersurface singularity is LNE if and only if its projectivized
tangent cone has only ordinary singularities. This provides an infinite family
of LNE singularities which is radically different from the class of minimal
singularities.
