Let $E$ be a complex vector space endowed with a Hermitian metric, it can be seen as the complexification of a real vector space $E_R$, with its metric coming from an inner product on $E_R$. Let $X$ be a partial flag variety over $E$ of some fixed dimensions $d_1< \cdots < d_s$.

The subset of flags that are complexifications of real flags is Zarisky dense in $X$.