A 'reduced' action formulation for a general class of the supergravity solu
tions, corresponding to the 'marginally' bound 'distributed' systems of var
ious types of branes at arbitrary angles, is developed. It turns out that a
ll the information regarding the classical features of such solutions is en
coded in a first-order Lagrangian (the 'reduced' Lagrangian) corresponding
to the desired geometry of branes. The marginal solution for a system of N
such distributions (for various distribution functions) span an N-dimension
al submanifold of the fields' configuration (target) space, parametrized by
a set of N independent harmonic functions on the transverse space. This su
bmanifold, which we call the 'H-surface', is a null surface with respect to
a metric on the configuration space, which is defined by the reduced Lagra
ngian. The equations of motion then transform to a set of equations describ
ing the embedding of a null geodesic surface in this space, which is identi
fied as the H-surface. Using these facts, we present a very simple derivati
on of the conventional orthogonal solutions together with their intersectio
n rules. Then a new solution for a (distributed) pair of p-branes at SU(2)
angles in D dimensions is derived. (C) 1999 Published by Elsevier Science B
.V.