  A theory of gravity in higher dimensions is considered. The usual
Einstein-Hilbert action is supplemented with Lovelock terms, of higher order in
the curvature tensor. These terms are important for the low energy action of
string theories.
  The intersection of hypersurfaces is studied in the Lovelock theory. The
study is restricted to hypersurfaces of co-dimension 1, $(d-1)$-dimensional
submanifolds in a $d$-dimensional space-time. It is found that exact thin
shells of matter are admissible, with a mild form of curvature singularity: the
first derivative of the metric is discontinuous across the surface. Also, with
only this mild kind of curvature singularity, there is a possibility of matter
localised on the intersections.
  This gives a classical analogue of the intersecting brane-worlds in high
energy String phenomenology. Such a possibility does not arise in the pure
Einstein-Hilbert case.
