  Complete intersections inside rational homogeneous varieties provide
interesting examples of Fano manifolds. For example, if $X = \cap_{i=1}^r D_i
\subset G/P$ is a general complete intersection of $r$ ample divisors such that
$K_{G/P}^* \otimes \mathcal{O}_{G/P}(-\sum_i D_i)$ is ample, then $X$ is Fano.
We first classify these Fano complete intersections which are locally rigid. It
turns out that most of them are hyperplane sections. We then classify general
hyperplane sections which are quasi-homogeneous.
