  The family of varieties of minimal rational tangents on a quasi-homogeneous
projective manifold is isotrivial. Conversely, are projective manifolds with
isotrivial varieties of minimal rational tangents quasi-homogenous? We will
show that this is not true in general, even when the projective manifold has
Picard number 1. In fact, an isotrivial family of varieties of minimal rational
tangents needs not be locally flat in differential geometric sense. This leads
to the question for which projective variety Z, the Z-isotriviality of
varieties of minimal rational tangents implies local flatness. Our main result
verifies this for many cases of Z among complete intersections.
