  We obtain a result about propagation of geometric properties for solutions of
the non-homogeneous incompressible Euler system in any dimension $N\geq2$. In
particular, we investigate conservation of striated and conormal regularity,
which is a natural way of generalizing the 2-D structure of vortex patches. The
results we get are only local in time, even in the dimension N=2; however, we
provide an explicit lower bound for the lifespan of the solution. In the case
of physical dimension N=2 or 3, we investigate also propagation of H\"older
regularity in the interior of a bounded domain.
