  We propose a precise definition of multidimensional fluids generated by
self-gravitating extended objects such as strings and membranes: a
p-dimensional perfect fluid is a smooth involutive p-dimensional distribution
on a spacetime, each integral manifold of which is a timelike, connected,
immersed submanifold of dimension, p -- representing the history of a
(p-1)-dimensional extended object. This geometric formulation of perfect fluids
of higher dimensions naturally leads to the associated stress-energy tensor.
Furthermore, the laws of temporal evolution and symmetries of such systems are
derived, in general, from the Einstein field equations and the integrability
conditions. We also present a matter model based on a 2-dimensional involutive
distribution, and it is shown that the stress-energy tensor for
self-gravitating strings gives rise to a non-trivial spherically symmetric
spacetime with a naked singularity.
