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Let $\Gamma$ denote a lattice in $SU(1,p)$, with $p$ greater than 1. We showthat there exists no Zariski dense maximal representation with target $SU(m,n)$if $n>m>1$. The proof is geometric and is based on the study of the rigidityproperties of the geometry whose points are isotropic $m$-subspaces of acomplex vector space $V$ endowed with a Hermitian metric $h$ of signature$(m,n)$ and whose lines correspond to the $2m$ dimensional subspaces of $V$ onwhich the restriction of $h$ has signature $(m,m)$.

Maximal representations of complex hyperbolic lattices in SU(m,n)