  A higher dimensional frame formalism is developed in order to study
implications of the Bianchi identities for the Weyl tensor in vacuum spacetimes
of the algebraic types III and N in arbitrary dimension $n$. It follows that
the principal null congruence is geodesic and expands isotropically in two
dimensions and does not expand in $n-4$ spacelike dimensions or does not expand
at all. It is shown that the existence of such principal geodesic null
congruence in vacuum (together with an additional condition on twist) implies
an algebraically special spacetime. We also use the Myers-Perry metric as an
explicit example of a vacuum type D spacetime to show that principal geodesic
null congruences in vacuum type D spacetimes do not share this property.
